DADT = Don't Ask, Don't Tell.
I'm Guy's secret, but he isn't married. His ex-wife refuses to accept that their divorce means he--and she--can date people, and has told him if she finds out he has any girlfriend, she won't let him be around her and their son. She's the only one I'm a secret from in his life, though. As long as it doesn't interfere with his relationships with his kids, he says he doesn't care who knows. And he says he'll deal with it if his ex finds out; he won't lie to keep our relationship hidden, he just doesn't talk about it around her. I don't really have a problem with that, since I'm not openly poly and Hubby is concerned about word getting back to his family or to my ex-husband.
I don't have any experience like you're asking for, Tigger, so I won't add to this; the only time I've been involved with a married man was a situation where his wife set it up, so obviously I wasn't secret and he wasn't cheating. My personal preference, like others who have responded, is to steer far clear of any man who's cheating on a partner.