Been there, done that.
Or something similar.
A jealous husband will believe what they want to believe, even if evidence to the contrary is right in front of them.
Mine was convinced that I was having an affair. So convinced that he was reading my journals behind my back, looking for proof.
There was no proof because there was no affair.
He reached the same conclusion yours did. His belief that I was cheating was so strong that he convinced himself it was true.
He tormented me about the affair that I wasn't having. He made me so miserable for so long that I got into therapy and then filed for divorce.