I agree with you Louisa111, what if he's NOT cheating?
I'm sorry, but maybe he just doesn't want to get too embroiled into a 'Facebook life' and just wants to use it, as my OH does, for daft videos and chatting to friends... without significant evidence of cheating you could be ending a relationship essentially because he doesn't want to be tagged in Facebook posts! Does nobody see how stupid that sounds???
He could just be getting arsey because he's sick of being followed around on facebook. We all need our own space, and maybe this is his outlet for that??
I'd really suggest having a talk and saying that his insistence on avoiding you on facebook makes you think he's either embarrassed by you or he's hiding something, and that hurts you. Then suggest closing both of your Facebook accounts as it's causing too much aggro for the relationship. Its just not worth it. After all its not like he uses Facebook for anything important or family-related is it? I'm sure he could do without it!
If he refuses for the sake of your marriage then I'd say he's being very unreasonable and your gut instinct is probably right. Start looking for actual evidence of cheating and start preparing to end the relationship, ensuring your financial stability as pp have suggested...
But if he's willing and understands you have nothing to worry about.
But if you go in all guns blazing ending a relationship calling him a cheat because he doesnt want to be tagged on facebook, with no actual evidence you're gonna look a bit mental IMO. If he is having an affair but you can't actually prove it, and you kick him out, you could push him straight into the arms of his mistress. And then in a divorce case he can say he only started this relationship AFTER you threw him out - and you will have no evidence to disprove it.
If you really think he's cheating start digging, get some evidence THEN tell him to sling his hook and serve him with divorce papers! Keep your dignity, don't let him make you look like a fool by throwing around empty accusations...