Cheating? Affair? Thoughts?

So about a year and a half ago (July 2017) I moved out of the home I shared with my husband. There were a multitude of reasons but the main one was because our eldest (mine, not his) son was going to private school on a full scholarship and our schedule didn't allow for us to drop him off and pick him up everyday. I got a small apartment near his school and made it work. I came home (at first) every weekend and if his father had him, I'd be home at that time too. Over time I got busier and would be home every other weekend. In April I decided I was tired of the separation and started moving back. I was hired by the local Uni and that elongated my move. Half of my stuff was at home with my husband and half was in storage. In June I was sent to another state by the Uni to finish research. Unbeknownst to me, my husband had decided that we were no longer together because I had abandoned the home and slept with a co-worker (2x). I had been with him days before he slept with her and days after too. I came home late one night (to surprise him) and there she was (didnt know who she was) at 11pm talking to my husband on my sofa. Didnt think much at the time, they are both field trainers and travel so they said she had just arrived from a trainung appointment from out of town. I suspected something (girl intuition) but when asked he denied anything happened. As she left that night she said "it was nice meeting you", This was in June 2018. About a week later he tells me he had at one point decided to leave me and had started seeing someone and did sleep with her, I asked if it was her and he said he didnt want to tell me who it was. Slowly over the months it became clear that it was her. 2 days after I came home he spoke to her and told her he was going to work on his marriage with me. They stopped communicating completely about 2 weeks after I came home, even at work its short. I saw her for the first time (since june 2018) this past Saturday and again yesterday. She knew he was married and still came to my house, he knew he was married and still invited her. I dont know what to do. Ive been home for 7 months and now I am forced to see her and it boils my blood. Hes not innocent, ive asked him why he didnt just tell me that he was done and he always says "would you have preferred that I left you and not tried to fix things" my answer is always yes, heart break kills. I know I abandoned the home so part of this is my fault but we had been trying for 2 months to get me home at the time he was with her. Was this cheating? Was it an Affair? Advice?