What do you think?

I need some outside perspective on my current situation. My husband and I have been together 10 years, married 2. We have a 9 year old and a 10 month old. This morning I thought I saw a message with the word "kiss" in it on his phone and after he dozed off it was bothering me so I looked at his texts and a girl listed as "Cassiopeia" had texted him "that kiss was.." I was shaking and copied down the number. I drove him to work because we have one car and I needed to get our 9 year old from her grandma who she stayed to visit with after Thanksgiving. I mulled over things all day and in the afternoon I texted confirming that I had the right person and then told her who I was and that I was the wife of the man she kissed and it was unacceptable. She agreed with me and asked to call me so I waited until I could get away from the kids and called her. She told me she believed we were in an open marriage, because he told her he goes home and tells me everything he does. He does say this to me too because he tells me all his adventures after he goes out to karaoke, which is a hobby of his and a friend hosts at a few bars. She said she was under the impression that he made out with some other girls but hadn't seen or heard anything specific. She told me they kissed inside the bar and again made out again outside. She was very remorseful and apologized to me and repeated that she thought we were non monogamous. She told me she'd have no more contact with him and would block him. After I picked him up from work and our 9 year old went to bed I asked him to tell me about his evening after we came home from his brother's and he went out again. He told me his whole evening and then said a girl he didn't recognize kissed him and then walked away. Tried to continue the story and gloss over this part. I stopped him and asked about the text message, clearly he knew her and had texted her prior to that evening so big bullshit. He told me backstory on how he knew her and some interactions he had with her previously, still framed it as she kissed him and he didn't stop her and didn't mention making out more another time that same night. I then told him I spoke to her on the phone and she told me they made out multiple times that night and her belief he was in an open relationship. He blamed her, being emotionally raw from thanksgiving events, and alcohol and I had to actually ask him before he said he was sorry. Before that he told me SHE was only sorry because SHE got caught. He got mad but shut up when I corrected him that he kissed her too and we're not doing that bullshit of saying she just kissed him, TWICE. He promised me it never happened before and he's never slept with anyone but me. He talks so much about other people respecting our marriage and him ducking flirtation to avoid drama that the hypocrisy is astounding. Him acting normal all day, trying to shift blame, and lying about the events are huge red flags to me and I'm questioning everything. I adore this man, and I want to make my marriage survive this. They both stated it was only kissing. Thank you if you read all that, I have no one to talk to and really needed to get it out. What do you think? How do I get through this?