Husband bought a house without me

My in laws have been pressuring my husband to buy a house near them. We always turned them downs because we weren’t financially ready at the time. We have been saving up for a down payment and honestly didn’t like the idea of living so close by them. We live in NYC and houses here are very small and expensive(Over 700,000) compared to the houses you can get out of state. I always wanted to move to Monroe or New Jersey and we had plans on buying a house in 3 years. Well like always my in laws heard of a house for sale near by and they went and took my husband to go see the house without me. That really got me so pissed off because if there’s plans to buy a house I should be involved too, but nobody took that into consideration not even my husband whom I just found out cheated on me not too long ago. Well after I threatened my husband to divorce him if he got the house my in laws chose for him he quickly changed his mind and told his parents he wasn’t going to get it. His parents had already told the owners of the house yes to it because they were sure my husband was going to say yes. They ended up having to buy it themselves with there savings. They gave us the silent treatment and my husband felt so guilty about them putting all their savings that he told them we’ll rent it from them and pay the mortgage so they wouldn’t have to worry about the mortgage because they already own several houses too and another house just adds more stress. I agreed because we live in an apartment and have 2 kids so a bigger house is nice to have or at least rent like I thought.... wrong!! My husband secretly put his name on the deed with his parents and lied to me about it. He thinks I’m stupid and don’t know the house will be in his name because he’s scared If we end up divorced i will want to have it. I read an Email in which names all 3 of them on the deed. My question is if anyone knows if I do end up divorcing him will I have rights to the house as well. The mortgage monthly will be 4,000 which I will be expected to pay half because my husband can not afford it by himself. Paying for this house is putting all my plans on hold including more kids, finishing school because I cannot afford to pay for it all. I’m scared that 5 years from now after paying up for the house my husband will kick me out or leave me because right now he cannot he trusted. He’s a liar and if he cheated once I’m sure he’ll do it again.