When I had Mice in the past I caught them in those (less inhumane) live traps and released them outside, got a few of those ultrasonic plug devices (which apparently turn all of your house's wiring into an impenetrable ultrasonic barrier, but that might annoy your dog) and probably most importantly, I stopped leaving out food for them.
I know releasing them at the end of my garden isn't effective in making them disappear, but it's a good way of dealing with them in the short term.
I'm not certain which was most effective, the ultrasonic plug devices or the fact I no longer collect my vegetable cuttings and compost bits in a bin in the kitchen before putting them outside, but since I plugged in those devices and cut out a stage in my compost routine I haven't had any Mice (or signs of Mice) in my house.
I live in the country so they're unavoidable and I frequently see them in the compost bin in our garden when I put stuff in it, but I haven't had any in the house for a long time.