You can use QuickTime Kit's capture APIs to record a movie of the audio, and QTMovie (from the same framework) to convert it to a more conventional format for audio files and to play back both the intermediate file and the converted file.
There used to be a QuickTime Kit Programming Guide, but it didn't cover capturing and is now gone from developer.apple.com. You should file a bug against the docs.
This answer will work in a Cocoa (Mac) app. If you meant to ask about the iPhone, you should re-tag your question, as the solution will be completely different for a Cocoa app vs. a Cocoa Touch (iPhone) app.