<human>: Could you distill the essence of the text into 1-3 sentences?

When I started spending time with who would eventually be my boyfriend, he was getting over a girl who he had dated for 2.5 years who dumped him out of the blue about 8 months prior to that. I was also getting over someone, we became close friends, and ended up dating. We like each other a lot, we usually do really well talking through issues that come up, and I'm really thankful for that. 

One thing that keeps causing issues for us, though, is that he keeps in contact with his ex-girlfriend. Not super close contact, they don't talk on a regular basis, but he almost always hangs out with her one or two times whenever she visits home. 

My boyfriend and I have talked about this a few times, I've told him that it makes me uncomfortable, and he says he is totally willing to cut off all contact if it will make me happy. I've never read their messages, but he doesn't keep a lock on his phone and has on several occasions told me that I could. 

So my question is, is this normal? My ex-boyfriend and I had a similarly sticky breakup, and we are not on good terms. It's hard for me to understand how he has totally forgiven her for breaking his heart for any other reason than still having feelings for her. I also feel like telling him to cut off contact is a little harsh, and totally not something I'm comfortable doing. Any advice?
<bot>: Boyfriend still hangs out with ex who broke his heart, insists that they are just friends, I need some sage advice