can you get out of a lease?

We are renting a house for $850/month. Which is expensive for where we live and what we make. We have a daughter who is 10 months old. Our heat is messed it. It turns on and off when it shouldn't. We turn it to 70, it only gets to 60. The thermostat is coming off the wall making it messed up because it's not level. There have been times where my daughters feet have turned purple even while in a sleeper because the heat would turn off at night.
The ceiling fan and lights we cant use because it shakes and that's dangerous. The other lights dont work anymore. One day they sparked and went out. The flooring is coming up. Some of the outlets dont work. 
It's a very nice house. But these things make it dangerous and not worth it. We have told our landlords and they don't fix it. During the summer we cant have the door open because the screendoor is broke and bees come in. They bought a door a year ago and still refuses to put it on.
Because they aren't fixing anything, can we get out of our lease somehow without it being on our record as an eviction? We have talked to them and they wont let us out. But because i feel its unsafe for our daughter, i want to leave. Who can we call to terminate the lease with no penalty? 
My husband is also in the military and they said if he gets stationed or deployed they will let us out. Its to the point that my husband wants to lie and said he's getting stationed somewhere. But, obviously that wont work because they will ask for paperwork.