What would you do in this situation? need advice

as a woman you right to feel disgusted but my advise is,if he is supporting both you and the baby give him a blind eyes and deaf ears....assume what he is doing is right a day will come and he will regret

The point is why he doing this ,you should have conversation him without pressure! I am married and and the best thing that made my relationship strong is neutral conversation on such issues that causes problems .So sit with him feel relax and have chat about his issues listen to him why he is doing this tell him your point why you don't like this .Come to a mutual understanding and believe me it will be all good at the the End
you have to take steps to make this relationship go,

I agree that you shouldn't push the panic button or do anything drastic, but I don't think you have the main responsibility to make this situation right. I think you should ask to have a serious talk with him and tell him that this is something that is not acceptable in a committed relationship, that it hurts your trust for him, and that you would like him to stop. I think you can judge what to do next by how seriously he takes your request for him to stop it. If he understands this hurts you and promises to stop - problem solved. If he is angry or resistant to changing his behavior, you might want to think about seeking counseling alone or together with him. And if he blames it on you and refuses to listen or seek counseling, you may have to at least think about whether he is a good man to partner with for the resto of your life - children or no children. It's your life, too.