It sounds like you don't even want to be married to him regardless of if he's been unfaithful.
(Wo)man up and talk to him about this. There is seriously no point in you both remaining married if he's sitting around secretly thinking about cheating on you and you're sitting around hoping he will just so you have an excuse to leave. Why not just call it a day and move on so you both can go live lives that you're actually interested in living?
Out of curiosity, though, you've been married less than a year and you already both seem uninterested in being married ... so what possessed you both to tie the knot in the first place?