Is my boyfriend gay?

I am in a serious relationship with a man I fear is gay. We were together for 3 years then it ended. During a fight at the end he told me he was bi sexual . He went on to tell me 6-7 years ago he had gay experience with men and then never wanted to do that again ... He has always been with and attracted to girls. We were apart for two years . He tried to get me back the entire time. Then I did . But I creeped his email and found that while we were apart he was messaging gay men and trans online when he was drunk. He insists he's not gay he has been curios but not gay. He insists he loves me , he is 36 if he was gay he would come out with it. We have great sex he always gets off and always wants it. Is it possible that he's not gay ?