If he is convinced you are cheating when you're not, and you're finding it impossible to explain that to him, I would recommend doing what I do in situations like that: give him an ultimatum.

Say something like: "I really really do love you and I swear with my entire heart that I am not cheating on you, but if you cannot trust my word on this then we are in a trust-less relationship and I can't live in one of these. Either you believe me and we continue, patching up what difficulties we may have along the way, like most couples have to do at some point, or you don't believe me - if that is the case then this relationship must come to an end."

Straight to the point, entirely honest, letting him know what could happen while still letting him know you love him.

Good luck! Hope everything goes well