My boy friend talk to his ex every time we argue ?

Sorry about my English, it’s not my first language. 

My boyfriend (father of my new born baby still talk to his ex, I have told him several times that It hurt me , but he gets mad because he said that they are really good friends. I asked him to introduce us but he said he don’t even see her... They don’t see each other , but every time we have an argument He reach out to her. Recently I told him that I couldn’t do it , I tried to be okay with there friendship but I’m really not. I told him that I had to remove myself. He decided then that he wasn’t going to talk to her anymore. Now today we had an argument and he called her and talked to her for a very long time. I feel disrespected.  I’m trying to keep my cool and act like a lady But it’s really hard. . What should I do ?