This isn't my definition of "being faithful," even though he thinks otherwise. He put his arm around her which is totally unacceptable. An emotional affair is in the works here, and if you can't make him see how out of line he's behaving, then it's a lost cause. He should be respectful enough to you; his fiance, and this woman's husband by ceasing contact. He's leading her on because she is clearly interested (if it's even true those feelings are not being reciprocated by him).

Tell him it's either you or her. Don't stand for this crap. Ask him how he would feel if you were engaging in such behavior.