Do you feed inside the coop? If so, mice (and rats) come for the chicken feed the birds tend to spill all over the place. Remove the feed and what else is there for them?
So move feed outside and/or secure it at night. If it must stay indoors, try a rat proof feeder. Some of them work really well to allow the chickens to eat, but deny rats, mice and wild birds like starlings (flying rats) access to the feed, so those move on or never come in the first place. BTW, simply taking the feed up at night is not good enough if there is an abundance of spilt feed on the floor.
Aside from all the other obvious issues with rats and mice, there may be another subtle issue that is most important of all. There are predators like weasels and snakes that dine almost exclusively on rats and mice. A large concentration of rats and mice living in or near the coop may well attract these other predators who arrive for the rats and mice, but are opportunistic killers who easily transition to the birds.