Being friends/friendly with your SO ex

Hey so I just wanted to post this because I wanted some other people's opinions and/or stories about a situation I am going through. My boyfriend of almost seven months is still close to his ex. They dated for almost four years and broke up maybe three months before we started dating. When we first started dating he would talk about her (his ex) a lot, and text her, and he is still in contact with her family. They are part of the same friend group and sometimes hangout with each other that way, but nothing just themselves. I can't help but be jealous, or avoid going to parties/things I know she will be at. He, however, thinks this is normal. I trust him with my whole heart, I just don't think it's important for me to get to know her. Thoughts?