Are you recording and streaming live? If not, you can mix audio in audacity (or sox) (or ....). And swap audio tracks with the video (or audio only) podcast.
$ audacity main_audio.wav
File -> Import -> Audio -> other file
do some edits, adjust gain, whatever...
Edit -> Select -> All
Tracks -> Mix and Render
If things aren't the way you like it, use and abuse Edit -> Undo
One of many ways. What music are you trying to capture? And why use a mic, if it's the computer playing it? There are ways to record the soundcards output without using a mic. Or just copy the files from the browsers cache. (about:cache). Many means to an end.