By this I mean a distro that does not use pulse audio at all. So when you are runing programs like
mumbles you do not lose audio playback becuase Jack took over the audio stack.
Ubuntu Studio should be what you're looking for. It's a multimedia oriented distro based (obviously) on Ubuntu which uses a realtime kernel and the JACK Audio Connection Kit.
puredyne is made specifically for multimedia applications based on Ubuntu and Debian Live that can run from a CD or DVD, but it does not automatically start up Jack.
There are several other distros for multimedia production, but as far as I know, none of these start Jack by default, and I do not know the state of development on these distros, so I include these just for completeness:
A different solution would be to tell Pulseaudio to run on top of Jack, if you are inclined to do some editing on your config files: http://trac.jackaudio.org/wiki/WalkThrough/User/PulseOnJack