Now I know that it is all going to come down to how convinced you actually are that he is being infaithful etc....but assuming that you have no proof, and there are 100% rationale (probably more rationale than what you are thinking) explainations for all you suspicions.
So when he says "honestly love there is nothing going on"....well he is hardly going to say much else if he wants to cover up is he....so his promise isn't IMO enough.
So what (if anything) could convince you (i.e. me) that it is all in my head?