Listener question: how to understand betrayal?

Listener question: My husband had a primarily emotional affair with his HR director. The flirting started pretty much right when he met her, then 6 months later it ballooned into an actual affair (not sex but kissing) and then I found out and we hashed things out for 6 weeks and he stopped the affair for a couple weeks. Then he started it back up for another 3-4 months but just texting. Nothing physical. Finally, about 4 months ago he really ended it. And he is working really hard on us. Genuine heartfelt apologies, spending lots of time together, talking and planning our lives, etc.

However, he still works closely with her. They have meetings most days and often several times a day. I know their meetings are not just business. I know he spends lots of time just catching up and chatting about her life and his. Full disclosure, he is a very chatty, friendly, engaging kind of boss with many of his team. So it would be a little unnatural for him to really pull back completely.

But I of course hate it. I hate that he still chats with her daily, I hate that she is his "confidant" which he justifies because as his director of HR, they have to discuss all the employees and new hires etc. I hate that he keeps me so separate from her. I'm not sure what would be normal there, but I know for sure he will mention my name when talking to other employees but never with her.

Basically, I am insecure and worried about their relationship but he insists that it is necessary for work. 

I just don't know what to do. I am constantly tempted to ask him what's going on with him and her. I am tempted to look at his messages. Eavesdrop on his calls. And of course always wanting to know where we stand and my favorite, "How could you??"

Does this perspective offer insights into how I should be making sense of this situation? If I was really free and anchored in my true beautiful self would I be so insecure and suspicious and jealous? Or is is actually wise, strong to ask to see his messages and demand he minimize his interaction with her?