CONSOLE_HTML_FORMAT = """\
<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<style>
{stylesheet}
body {{
    color: {foreground};
    background-color: {background};
}}
</style>
</head>
<body>
    <pre style="font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace"><code>{code}</code></pre>
</body>
</html>
"""

CONSOLE_SVG_FORMAT = """\
<svg class="rich-terminal" viewBox="0 0 {width} {height}" xmlns="http://www.w3.org/2000/svg">
    <!-- Generated with Rich https://www.textualize.io -->
    <style>

    @font-face {{
        font-family: "Fira Code";
        src: local("FiraCode-Regular"),
                url("https://cdnjs.cloudflare.com/ajax/libs/firacode/6.2.0/woff2/FiraCode-Regular.woff2") format("woff2"),
                url("https://cdnjs.cloudflare.com/ajax/libs/firacode/6.2.0/woff/FiraCode-Regular.woff") format("woff");
        font-style: normal;
        font-weight: 400;
    }}
    @font-face {{
        font-family: "Fira Code";
        src: local("FiraCode-Bold"),
                url("https://cdnjs.cloudflare.com/ajax/libs/firacode/6.2.0/woff2/FiraCode-Bold.woff2") format("woff2"),
                url("https://cdnjs.cloudflare.com/ajax/libs/firacode/6.2.0/woff/FiraCode-Bold.woff") format("woff");
        font-style: bold;
        font-weight: 700;
    }}

    .{unique_id}-matrix {{
        font-family: Fira Code, monospace;
        font-size: {char_height}px;
        line-height: {line_height}px;
        font-variant-east-asian: full-width;
    }}

    .{unique_id}-title {{
        font-size: 18px;
        font-weight: bold;
        font-family: arial;
    }}

    {styles}
    </style>

    <defs>
    <clipPath id="{unique_id}-clip-terminal">
      <rect x="0" y="0" width="{terminal_width}" height="{terminal_height}" />
    </clipPath>
    {lines}
    </defs>

    {chrome}
    <g transform="translate({terminal_x}, {terminal_y})" clip-path="url(#{unique_id}-clip-terminal)">
    {backgrounds}
    <g class="{unique_id}-matrix">
    {matrix}
    </g>
    </g>
</svg>
"""

_SVG_FONT_FAMILY = "Rich Fira Code"
_SVG_CLASSES_PREFIX = "rich-svg"

rich/_export_format.py
CONSOLE_HTML_FORMAT = """\
<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<style>
{stylesheet}
body {{
    color: {foreground};
    background-color: {background};
}}
</style>
</head>
<body>
    <pre style="font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace"><code style="font-family:inherit">{code}</code></pre>
</body>
</html>
"""

CONSOLE_SVG_FORMAT = """\
<svg class="rich-terminal" viewBox="0 0 {width} {height}" xmlns="http://www.w3.org/2000/svg">
    <!-- Generated with Rich https://www.textualize.io -->
    <style>

    @font-face {{
        font-family: "Fira Code";
        src: local("FiraCode-Regular"),
                url("https://cdnjs.cloudflare.com/ajax/libs/firacode/6.2.0/woff2/FiraCode-Regular.woff2") format("woff2"),
                url("https://cdnjs.cloudflare.com/ajax/libs/firacode/6.2.0/woff/FiraCode-Regular.woff") format("woff");
        font-style: normal;
        font-weight: 400;
    }}
    @font-face {{
        font-family: "Fira Code";
        src: local("FiraCode-Bold"),
                url("https://cdnjs.cloudflare.com/ajax/libs/firacode/6.2.0/woff2/FiraCode-Bold.woff2") format("woff2"),
                url("https://cdnjs.cloudflare.com/ajax/libs/firacode/6.2.0/woff/FiraCode-Bold.woff") format("woff");
        font-style: bold;
        font-weight: 700;
    }}

    .{unique_id}-matrix {{
        font-family: Fira Code, monospace;
        font-size: {char_height}px;
        line-height: {line_height}px;
        font-variant-east-asian: full-width;
    }}

    .{unique_id}-title {{
        font-size: 18px;
        font-weight: bold;
        font-family: arial;
    }}

    {styles}
    </style>

    <defs>
    <clipPath id="{unique_id}-clip-terminal">
      <rect x="0" y="0" width="{terminal_width}" height="{terminal_height}" />
    </clipPath>
    {lines}
    </defs>

    {chrome}
    <g transform="translate({terminal_x}, {terminal_y})" clip-path="url(#{unique_id}-clip-terminal)">
    {backgrounds}
    <g class="{unique_id}-matrix">
    {matrix}
    </g>
    </g>
</svg>
"""

_SVG_FONT_FAMILY = "Rich Fira Code"
_SVG_CLASSES_PREFIX = "rich-svg"

rich/_export_format.py
diff --git a/CHANGELOG.md b/CHANGELOG.md
index f68d33c02..3562f6df6 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -11,6 +11,10 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 - Adds missing parameters to Panel.fit https://github.com/Textualize/rich/issues/3142
 
+### Fixed
+
+- Ensure font is correctly inherited in exported HTML https://github.com/Textualize/rich/issues/3104
+
 ## [13.6.0] - 2023-09-30
 
 ### Added
diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md
index bff51eea3..ba8759eae 100644
--- a/CONTRIBUTORS.md
+++ b/CONTRIBUTORS.md
@@ -73,3 +73,4 @@ The following people have contributed to the development of Rich:
 - [James Addison](https://github.com/jayaddison)
 - [Pierro](https://github.com/xpierroz)
 - [Bernhard Wagner](https://github.com/bwagner)
+- [Aaron Beaudoin](https://github.com/AaronBeaudoin)
diff --git a/rich/_export_format.py b/rich/_export_format.py
index 998a9b0de..e7527e52f 100644
--- a/rich/_export_format.py
+++ b/rich/_export_format.py
@@ -12,7 +12,7 @@
 </style>
 </head>
 <body>
-    <pre style="font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace"><code>{code}</code></pre>
+    <pre style="font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace"><code style="font-family:inherit">{code}</code></pre>
 </body>
 </html>
 """
diff --git a/tests/test_console.py b/tests/test_console.py
index a3b73793c..36d15df00 100644
--- a/tests/test_console.py
+++ b/tests/test_console.py
@@ -529,7 +529,7 @@ def test_export_html():
     console.print("[b]foo <script> 'test' [link=https://example.org]Click[/link]")
     html = console.export_html()
     print(repr(html))
-    expected = '<!DOCTYPE html>\n<html>\n<head>\n<meta charset="UTF-8">\n<style>\n.r1 {font-weight: bold}\n.r2 {color: #ff00ff; text-decoration-color: #ff00ff; font-weight: bold}\n.r3 {color: #008000; text-decoration-color: #008000; font-weight: bold}\nbody {\n    color: #000000;\n    background-color: #ffffff;\n}\n</style>\n</head>\n<body>\n    <pre style="font-family:Menlo,\'DejaVu Sans Mono\',consolas,\'Courier New\',monospace"><code><span class="r1">foo &lt;</span><span class="r2">script</span><span class="r1">&gt; </span><span class="r3">&#x27;test&#x27;</span><span class="r1"> </span><a class="r1" href="https://example.org">Click</a>\n</code></pre>\n</body>\n</html>\n'
+    expected = '<!DOCTYPE html>\n<html>\n<head>\n<meta charset="UTF-8">\n<style>\n.r1 {font-weight: bold}\n.r2 {color: #ff00ff; text-decoration-color: #ff00ff; font-weight: bold}\n.r3 {color: #008000; text-decoration-color: #008000; font-weight: bold}\nbody {\n    color: #000000;\n    background-color: #ffffff;\n}\n</style>\n</head>\n<body>\n    <pre style="font-family:Menlo,\'DejaVu Sans Mono\',consolas,\'Courier New\',monospace"><code style="font-family:inherit"><span class="r1">foo &lt;</span><span class="r2">script</span><span class="r1">&gt; </span><span class="r3">&#x27;test&#x27;</span><span class="r1"> </span><a class="r1" href="https://example.org">Click</a>\n</code></pre>\n</body>\n</html>\n'
     assert html == expected
 
 
@@ -538,7 +538,7 @@ def test_export_html_inline():
     console.print("[b]foo [link=https://example.org]Click[/link]")
     html = console.export_html(inline_styles=True)
     print(repr(html))
-    expected = '<!DOCTYPE html>\n<html>\n<head>\n<meta charset="UTF-8">\n<style>\n\nbody {\n    color: #000000;\n    background-color: #ffffff;\n}\n</style>\n</head>\n<body>\n    <pre style="font-family:Menlo,\'DejaVu Sans Mono\',consolas,\'Courier New\',monospace"><code><span style="font-weight: bold">foo </span><span style="font-weight: bold"><a href="https://example.org">Click</a></span>\n</code></pre>\n</body>\n</html>\n'
+    expected = '<!DOCTYPE html>\n<html>\n<head>\n<meta charset="UTF-8">\n<style>\n\nbody {\n    color: #000000;\n    background-color: #ffffff;\n}\n</style>\n</head>\n<body>\n    <pre style="font-family:Menlo,\'DejaVu Sans Mono\',consolas,\'Courier New\',monospace"><code style="font-family:inherit"><span style="font-weight: bold">foo </span><span style="font-weight: bold"><a href="https://example.org">Click</a></span>\n</code></pre>\n</body>\n</html>\n'
     assert html == expected
 
 
@@ -591,7 +591,7 @@ def test_save_text():
 
 
 def test_save_html():
-    expected = "<!DOCTYPE html>\n<html>\n<head>\n<meta charset=\"UTF-8\">\n<style>\n\nbody {\n    color: #000000;\n    background-color: #ffffff;\n}\n</style>\n</head>\n<body>\n    <pre style=\"font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><code>foo\n</code></pre>\n</body>\n</html>\n"
+    expected = '<!DOCTYPE html>\n<html>\n<head>\n<meta charset="UTF-8">\n<style>\n\nbody {\n    color: #000000;\n    background-color: #ffffff;\n}\n</style>\n</head>\n<body>\n    <pre style="font-family:Menlo,\'DejaVu Sans Mono\',consolas,\'Courier New\',monospace"><code style="font-family:inherit">foo\n</code></pre>\n</body>\n</html>\n'
     console = Console(record=True, width=100)
     console.print("foo")
     with tempfile.TemporaryDirectory() as path:

[BUG] `font-family` ignored in `html_export` due to user agent stylesheet for `<code>`
- [X] I've checked [docs](https://rich.readthedocs.io/en/latest/introduction.html) and [closed issues](https://github.com/Textualize/rich/issues?q=is%3Aissue+is%3Aclosed) for possible solutions.
- [X] I can't find my issue in the [FAQ](https://github.com/Textualize/rich/blob/master/FAQ.md).

**Describe the bug**

Run this code:

```py
import rich.console

try:
    test = 1
    raise Exception()
except Exception:
    console = rich.console.Console(record=True)
    console.print_exception(show_locals=True)
    html = console.export_html(inline_styles=True)
    with open("test.html", "w") as html_file:
        html_file.write(html)
```

You will get an `test.html` output file. Open it in Chrome.

I'm on macOS, and it shows up like this:

![image](https://github.com/Textualize/rich/assets/26592486/4b124132-b7a9-4156-bfd9-8912c65f2764)


Notice the lines are not aligned properly on the right side. Here is why:

![image](https://github.com/Textualize/rich/assets/26592486/8d6e13e6-2124-46e2-972d-1d4a31256615)

As you can see, Chrome's user agent stylesheet causes the `<code>` element to reset the `font-family` on the `<pre>` element back to `monospace`. All we need is to have Rich add a `font-family: inherit;` on the `<code>` element and everything is fine:

![image](https://github.com/Textualize/rich/assets/26592486/ed1c2e6e-7d89-4d39-8301-cc92679458d9)

**Platform**
<details>
<summary>Click to expand</summary>

What platform (Win/Linux/Mac) are you running on? What terminal software are you using?
Mac with Chrome

```
❯ python -m rich.diagnose
╭───────────────────────── <class 'rich.console.Console'> ─────────────────────────╮
│ A high level console interface.                                                  │
│                                                                                  │
│ ╭──────────────────────────────────────────────────────────────────────────────╮ │
│ │ <console width=148 ColorSystem.TRUECOLOR>                                    │ │
│ ╰──────────────────────────────────────────────────────────────────────────────╯ │
│                                                                                  │
│     color_system = 'truecolor'                                                   │
│         encoding = 'utf-8'                                                       │
│             file = <_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'> │
│           height = 87                                                            │
│    is_alt_screen = False                                                         │
│ is_dumb_terminal = False                                                         │
│   is_interactive = True                                                          │
│       is_jupyter = False                                                         │
│      is_terminal = True                                                          │
│   legacy_windows = False                                                         │
│         no_color = False                                                         │
│          options = ConsoleOptions(                                               │
│                        size=ConsoleDimensions(width=148, height=87),             │
│                        legacy_windows=False,                                     │
│                        min_width=1,                                              │
│                        max_width=148,                                            │
│                        is_terminal=True,                                         │
│                        encoding='utf-8',                                         │
│                        max_height=87,                                            │
│                        justify=None,                                             │
│                        overflow=None,                                            │
│                        no_wrap=False,                                            │
│                        highlight=None,                                           │
│                        markup=None,                                              │
│                        height=None                                               │
│                    )                                                             │
│            quiet = False                                                         │
│           record = False                                                         │
│         safe_box = True                                                          │
│             size = ConsoleDimensions(width=148, height=87)                       │
│        soft_wrap = False                                                         │
│           stderr = False                                                         │
│            style = None                                                          │
│         tab_size = 8                                                             │
│            width = 148                                                           │
╰──────────────────────────────────────────────────────────────────────────────────╯
╭─── <class 'rich._windows.WindowsConsoleFeatures'> ────╮
│ Windows features available.                           │
│                                                       │
│ ╭───────────────────────────────────────────────────╮ │
│ │ WindowsConsoleFeatures(vt=False, truecolor=False) │ │
│ ╰───────────────────────────────────────────────────╯ │
│                                                       │
│ truecolor = False                                     │
│        vt = False                                     │
╰───────────────────────────────────────────────────────╯
╭────── Environment Variables ───────╮
│ {                                  │
│     'TERM': 'xterm-256color',      │
│     'COLORTERM': 'truecolor',      │
│     'CLICOLOR': None,              │
│     'NO_COLOR': None,              │
│     'TERM_PROGRAM': 'vscode',      │
│     'COLUMNS': None,               │
│     'LINES': None,                 │
│     'JUPYTER_COLUMNS': None,       │
│     'JUPYTER_LINES': None,         │
│     'JPY_PARENT_PID': None,        │
│     'VSCODE_VERBOSE_LOGGING': None │
│ }                                  │
╰────────────────────────────────────╯
platform="Darwin"

❯ python -m pip freeze | grep rich
rich==13.4.2
```

</details>

