It's unusual for chickens NOT to kill mice.
Mice are only there because there's food, so deterrent is as important as capture.
Keep feed in metal bins, turn the 'bedding' in the coop daily, block any obvious entry points (difficult, I know).
These are great traps ...
http://tinyurl.com/2eyefaj ... but what are you doing with them once caught? Humane capture is great if you're then killing them, but letting them go at the end of the garden is, at best, futile.
You could make a 'bait' by mixing equal quantities of cornmeal and plaster of Paris. Put it under a metal bucket, leaving a slight gap.
The mice will eat it, it hardens in their stomach and they die. If the chickens then eat the mice (totally fine, they naturally do it anyway - or they should be) then the bait won't harm them.