How can I stop Snooping?

My husband and I went through a very rough patch during the first 5 mtns of our marriage. However, we made it through and we're currently doing really well. The reason why we went through the rough patch is because I found out that he was spending alot of his time talking to a girl that he said that is "a friend" but he's never introduced me to her. I started to get really suspicious so I decided to do some research and check his phone log. Come to find out, he was speaking to her every single chance that he got and this was never when I'm around. I also noticed that his phone would ring while I'm around and he would often ignore it and when I check his phone, the missed call would be from her. I confronted him about it again and he stated that there was nothing going on so I decided to call her to see if she was aware of me. When I spoke to her she sounded like a respectful person and she was really sincere, she apologized to me and let me know that all the phone calls will stop from her end and that she would never try to break up a happy home.

When my husband found out that I contacted this woman he got really mad at me and threatened to file for divorce. He slept on the couch for weeks voluntarily and no matter how much I begged and pleaded to him he was just not budging. Finally things started to go back to normal, we didn't go to councilling or anything because he refused to go. However, we managed to work it out so I decided to go behind his back and delete this woman's number out of his phone and block all text messages from coming in from her.

I check his phone bill every once in a while and I notice that he no longer speaks to this woman, however, I still don't trust him the way I used to. I still snoops around and search his phone sometimes and I really don't want to do this. I don't want to search but this situation has caused me to be somewhat insecure about our marriage. Any advice on how I can move on from this?