My neighbor lied to the police. What do we do?

My neighbour has not liked us since the moment we moved in. My dog barks (she's in a fenced backyard) His wife psychotically screams at her. The husband has been to my door twice once drunk telling me the neighbours all hate us and the neighbourhood was quiet before we moved in. He proceeded to tell me that I must keep my dog inside all day and put a muzzle on her or he would call the city. I told him no and he got angry. My dog barks about 4 or five times per day and for short periods and only at them when they're hanging out beside our gate. Then we had a fire in our firepit in our front yard not knowing that we couldn't burn in this area. He called the fire department on us (we had two small logs burning and nowhere near his property) and they charged us 100 dollars. That was the last straw. My husband got angry and yelled at him to come over and apologize to me for the drunken visits and to stop screaming at the dog. He told him to put his kids inside and to come over and talk about it instead of hiding in his house phoning people. He did NOT go on his property or harm in any way. The neighbour then called the police and told them a bold faced lie. He said my husband threatened to kill his kids!!!! The police arrested my husband and now he has to go to court!! I heard the whole conversation and so did our tenant and her boyfriend downstairs! What do we do?? Can we turn around and charge him with slander? I'm at the end of my rope with this guy and I need to get him back. He's ruining our lives!!