Read up on Joel Salatin's setup....he's been keeping chickens under rabbits for many years now and describes the benefits in his book.
I used to have chickens under our rabbits and it is a win/win situation....and absolutely no illness resulted in this setup. The chickens benefit from the dropped feed and they mix the droppings into the bedding, keeping ammonia odors from the urine all dispersed into the same bedding. When you finally clean out this bedding, the chicken manure is cooled down by the rabbit droppings, making composting a little quicker....great for the garden!
If you really want to make a great combo, build a box under your cages into which the droppings can fall, place hardware wire over the box and keep earthworms in the bedding/feces. Then you can supply your chickens with the extra protein. A lot of people are diversifying their livestock in this manner and find the benefits to be wonderful.
