Is this cheating and should I forgive him?

My husband and I have been separated about a month while he decides what he wants. He hasn't filed for divorce yet, he was trying to have some time alone to decide what he wants to do, be together or get divorced. So, Friday night he got on Tinder, met a girl, went to her house to watch a movie. He says they started kissing and he started feeling horribly guilty and abruptly left. The next day we spent the day together with our son and he came clean. He said he was so sorry, he realized he didnt want anyone else, he wanted to be with me. So now I'm in this place where I dont know what to do. Turns out she is good friends with my sister, so I have the opportunity to get her side of the story if I want it (just to see if he told me the whole truth). What would you do? I respect him for being honest, but I want to know if he actually told me everything that happened. I think I would feel differently if he had sex with her. Any advice? I want our marriage to work, but if he slept with someone else... that's a big blow to come back from... ugh, help!

UPDATE: I talked to her. Her story matched his, they just made out and then he left abruptly. He has asked for forgiveness and said he would be willing to go to counseling with me to fix our marriage (he was not willing to go before this happened). I feel like he really realized he messed up and is trying to make things right to save our marriage. I fully believe in trying everything to save a marriage before giving up (except in cases of abuse), so I feel like I need to give him a chance. But I also feel stupid for giving him that chance...