It's fun to watch your application take shape. :-) I'm going to assume this is a follow-on to your last question and that you want to write C# code to accomplish this task. Are you still writing this into an AVI container? AVI stands for "audio/video interleaved" and is designed to transport both audio and video.
So, yes, you should be able to write both MJPEG and audio into an AVI file.
Guess what! You have lots of options for audio codecs too. We haven't cataloged quite as many audio codecs as video codecs (but close). Good news, though: Implementing a basic audio encoder in pure C# should be much simpler than trying to port even an MPEG-1 video encoder. Alternatively, check around to see if you can find an MP3 encoder written in pure C#. AVI accommodates MP3. If not, try IMA ADPCM. It's easy to implement and gives you 4:1 compression. Thus, if you have a monophonic, 44100 Hz, 16-bit stream, that requires 88200 bytes/sec. IMA ADPCM will give you roughly 22050 bytes/sec (plus small overhead).