I don't think you can do that.  If you are using the TV then it has "control" of the sound and wouldn't be able to use another media player.  Only one "media player" (in this case the TV) can have use of the sound playback. 

Try just turning down the volume in the TV player, while leaving it up in the music player. Don't try to mute the main volume control.

I don't have MCE, but I sometimes have a video playing in Windows Media Player, and listen to tunes in iTunes at the same time.

Val