You can do it if you've got multiple outputs on your soundcard.
I record music so I've got loads on mine but I bought a special, external soundcard.
If you haven't got multiple outputs I think you'd need to buy another cheap soundcard to go alongside your onboard sound, and use one for outputting the game sound and the other for the music.
If you have got multiple outputs download winamp. Then go in to Options -> Preferences -> Plug Ins -> Outputs -> Configure and then you can choose which output to play your music through.
You can download Winamp from here, it's free.
Winamp Download