The problem is probably the sound device getting locked by some app. There should be software, I believe, that let you use two (or more?) programs to produce sound at the same time, I just don't remember their names. But why on earth would you like to listen to mp3 while calling with Skype? I mean, doesn't the music disturb you?

Or your friend (on a regular phone the other end could possibly hear the music too, depending on the volume)