Makes no difference run what you want when they are not crossfired and using it for mining.
You can use LinuxCoin it's all been setup for you and it's small enough to run from a memory stick.
If you're gaming they have to be the same series and crossfired.
If not crossfired you game on the first card and the others can mine in the background without causing any lag.
Some people have noticed a drop in performance when crossfired, but I didn't.
I ran a 5870, 5850, and a 5830 in a Frankenfire 3 way CF. I didn't see hardly any drop in hashrate with or without CF. I ended up swapping the slower two and trying it with the 5870 and a 5970, and again CF made no difference.
But to answer the OP's question, yes, you can mine with different cards just fine. The only thing I would suggest is keeping 5xxx and 6xxx cards out of the same rig as any 7xxx cards, due to SDK incompatibilities. 7xxx cards require SDK 2.6 or newer, with 2.8 being the newest. However, 5xxx and 6xxx don't like anything past 2.5, and will run slower with the newer versions.