If I were you I'd ignore everything the guy above is saying. Regardless of where their relationship is, its NEVER a good idea to break someone up, emotionally or morally. The principle of 'if he'll cheat on her he can cheat on you' can be true. Likening it to divorcing someone is bollocks, as with splitting up, there's no deception. Both parties know where they stand.
If he feels the same about you as you do about him, why hasn't he called it a day with her? Sounds like he's having his cake and eying it at the moment. Getting the best of both worlds. I'd ask him outright how he feels, but don't do anything behind her back.

Put yourself in the gf's shoes... Would you be ok with someone else persuing your bf?