This is an OLD thread but honestly the most humane way to get rid of mice is snap traps.
I know people think that catching them and releasing them is humane but really it's not. You have to take the mice FAR away from your house or they'll re enter. When you do take them far away it is very stressful on the animal and you run the risk of introducing them into other colonies that are VERY territorial. Mouse fights are NOT pretty and they usually end in death. Also rodents learn their territory. They learn where things are such as food and predators. If you introduce a rodent into a new territory they won't know where predators are and they won't know where food it. They'll run a huge risk of starving to death or getting killed or injured by a predator.
Cats aren't a good idea either when it comes to deterring mice. They don't kill the mouse instantly, they just play with it, which can result in broken limbs and injuries.
I did hear that those ultrasonic things you plug into wall outlets do work, but they're not a good idea if you have other pets in the house. They'll just go insane by the noise.
If there is an infestation in the actual house, snap traps, if set correctly are very affective and they kill instantly. They break the vertibrae at the base of the skull, by the time the pain has registered the mouse is already dead. They aren't flawless but they do work most of the time.
I just want to add also that I don't like to see animals die but sometimes what looks to be the most humane way really isnt. Just my 2 cents