Normally, I'd provide a summary, but this bug is best described by a how-to-reproduce section.
Build latest Mumble (git describe says it's 1.2.3-184-gae54c0c) on Linux (Fedora 15 x86_64 here).
I expect Rhythmbox to continue playing, but become much quieter when I start speaking.
Rhythmbox mutes itself once Mumble opens! It unmutes itself when Mumble is closed.
The simplest workaround is to manually force Rhythmbox to play. Once it starts playing, things work as intended.
Rhythmbox is trying to respect a Pulseaudio setting. Mumble, as of git revision 1.2.3-58-ge6831d8, identifies itself as a phone application (see src/mumble/PulseAudio.cpp, line 115). Rhythmbox mutes itself as long as the "phone" audio is alive.
Rhythmbox is perhaps overzealous in muting itself so suddenly, but I think this is the correct behavior; if I received a call, I'd want my music to pause and mute. However, there's two reasons why this is Mumble's fault:
This mess is possibly a Pulseaudio missing feature more than anything else, but for the time being, Mumble should probably be more conservative with its role, lest more apps mistake a Mumble chatroom for a phone call.