Is having an unspoken “open” relationship normal? Help

I have been married in a gay relationship for 5 years. A few months ago i caught my husband cheating red handed when i was going through his phone . Our sex life isn’t the best at the moment so was i shocked ? Not really . Anyway it was obvious upon reading these messages that he only hits this person up for sex . And when i confronted him about this he confirmed that it was only a sex thing . I told him i wasn’t mad as long as he’s protecting himself and to not hide things from me. I asked him if he wanted an open relationship and i can tell he wants to say yes but he’s guilty or embarrassed or whatever . I told him to just tell me these things and not hide them from me and i won’t be mad.To tell you the truth i as well have thought about doing this . I love my husband , i don’t want to be with anyone else but him. But why does he feel the need to hide it from me ? Anyone i else has always been strictly sex . Has anyone else had a sinilar situation ?