If I may nisva.....
@Paulie...if you mean play the mp3 with media player as a background, but have another application recording your microphone, then yes.
If you are wishing to have software that "mixes" audio information, then I would suggest Mixcraft. It is not free, but it has a trial. You can mix down to MP3 for the first 10 or so days.
Have fun, and post back!