LSB steganography with pure Python
Performance:
def get_char(self):
    new_byte = ''

    for bit in range(0, 8):
        byte = self.fh.read(1)

        new_byte += str(ord(byte) &amp; 0x01)

    n = int(new_byte, 2)
    desteg_char = binascii.unhexlify('%x' % n)
    desteg_char = ''.join(map(chr, desteg_char))
    return desteg_char

This is not as simple as it could be. You are reading 8 bits as strings to build a single byte, converting it to an integer, then to a hex string (string format before unhexlify), then to a hexadecimal string, then mapping to a character, and then joining them together. I recommend doing more math and less string conversion and concatenation.
Style:
1. Use consistent string delimiters

You have ' in most places, like open(StegImageFile, 'rb'), but you also have DELIMITER = &quot;$&quot; and open(StegImageFile, &quot;wb&quot;). Use ' everywhere if that's what you're using.

2. Remove unnecessary parentheses

if (s_sz != ''): should be if s_sz != '':, or even more concise: if s_sz:.

3. Consider meaningful variable names

s_sz isn't a helpful variable name, and I don't know what it is at a glance, other than that it's the string form of sz (also not helpful).

4. Remove the space in print (text)

You don't use spaces after any other function names.

5. Remove weird leading spaces

The space before # Consts

The space before import binascii