Mine mix just fine.
I have chickens in a coop, and rabbits in hutches, and they share the same run area when they are loose.
Now, there are issues to be aware of. As someone else said, they don't - and shouldn't - eat the same food. In my case, I put the chicken food in the coop (where the rabbits cannot get to) and feed the rabbits in their special feeders in their hutches once a day. The food for the rabbits doesn't sit around all day for the chickens to even see. Eggs get laid in nestboxes in the coop, so I don't have problems with rabbits bothering eggs (breaking them, pooping on them) in any way.
Some days I throw some cracked corn or sunflower seeds into the run, and the chickens scratch around for them all day. The rabbits don't seem to care. They'd eat them if they were sitting in front of them, but they don't hunt around to find them.
Chickens do peck at rabbits, especially when the rabbits are first introduced. It does die down, but does not go away completely. And chickens peck more at smaller rabbits. I would NEVER leave baby rabbits where chickens could get them. EVER. I firmly believe the chickens would eat the babies. (They can eat mice, and baby rabbits aren't much bigger!) I don't even leave babies in hutches if the chickens are on the other side of the wire - chicken heads can reach an inch or two inside the hutches. Rabbits don't get to go in the run until they're 3-4 months old. They stay in hutches or overlarge pens - both outside the chicken run - until then, to keep them alive.
I do have one rabbit that wants to bully the chickens. And some day she might succeed. So be aware that might happen, too. If she's around when the chickens are scratching or drinking, one of these days she might try to take a bite out of a chicken comb. Time will tell.
The poop doesn't seem to be an issue. Rabbits get it on their undersides from time to time. But no biggie, it cleans off.
Have any specific questions? I'll answer them if I can.
