Husband keeps “Cyber Cheating”

My husband has been reaching out to prostitutes and woman since he came back from a deployment in 2015.. at first I thought it was just a phase but it has lasted since then until now. I noticed since it started overseas, I have been thinking that he had some sexual encounters but he wouldn’t admit it. Fast forward to today, I noticed that he has made a completely different Snapchat under a different name along with the app “kik” and craigslist. He has been even sending dick picks to random women saying he wants to fuck and have a good time.. even asked for a threesome. I found out he went on a dinner date with one of them but swears they didn’t have sex. At this point he’s a compulsive liar so I don’t know what to believe. We have been married for 5 years so I don’t know what going on at this point. He says he’s doing because he’s insecure with himself but I feel like it’s more. Does anyone know what could be gong on? We also have two kids and are getting ready to close on a new home but I don’t want to be in a home with a toxic environment.