I don't think this can be done solely within a PC, you may have to use an external mixer, even a small one would do.
I haven't tried it, but I suggest connecting your mic to one channel of the mixer, and the PC line-out to another channel.
The music would be generated on the PC using any music player, but you might find it worth looking at ZaraRadio for this.
Then connect the output of the mixer to the line-in of the PC. You must configure the Windows Recording Control to select line-in and NOT stereo mix (or similar names). The selection in Recording Control is the source for Broadwave's Live stream.
When your select Line-in for the Recording source, Broadwave Live relays the PC's input and not the sound generated on the Playback portion of the soundcard.