Separating integers substrings from those with alphabetical letters
The elif in


   if character in "0123456789":
        // ...
    elif character not in "0123456789":
        // ...



can be replaced by an else.


if string_type in ("Int", ""):
    current_substring += character
    if string_type == "":
        string_type = "Int"
else:
    character_list.append(current_substring)
    string_type = "Int"
    current_substring = character



can be simplified to

if character in "0123456789":
    if string_type == "Str":
        character_list.append(current_substring)
        current_substring = ""
    string_type = "Int"
    current_substring += character


and similarly for the non-digits case. However, using strings
("", "Str", "Int") for the current state is error-prone. 
An enumeration would be an alternative, or in this case simply a boolean:

in_digits = None
for character in input_text:
    if character in "0123456789":
        if in_digits is False:
            character_list.append(current_substring)
            current_substring = ""
        in_digits = True
        current_substring += character
    else:
    // ...


And now the two cases can be combined into one:

in_digits = None
for character in input_text:
    is_digit = character in "0123456789"
    if in_digits == (not is_digit):
        character_list.append(current_substring)
        current_substring = ""
    in_digits = is_digit
    current_substring += character


More remarks:


if not input_text:
    return None



When called with an empty string, I would expect the function to return
an empty array, not None.


character_list = []



The variable name is slightly misleading, this is a list of strings.

Summarizing the suggestions so far, we have

def separate_text(input_text):
    string_list = []
    current_substring = ""
    in_digits = None
    for character in input_text:
        is_digit = character in "0123456789"
        if in_digits == (not is_digit):
            string_list.append(current_substring)
            current_substring = ""
        in_digits = is_digit
        current_substring += character
    string_list.append(current_substring)
    return string_list


Finally note that the same can be simply achieved by splitting the
string on a regular expression:

import re

def separate_text(input_text):
    return [item for item in re.split('(\d+)', input_text) if item]