I would call it absolutely improper behavior. While it may be ok to behave like this if he was not in a commitment but if he is, this is IMPROPER and there are no two ways about it.Accept it or leave it. Don't expect him to change if he has not felt the need to change his behavior himself.
Actually i personally think his behavior is more an obsession- maybe there is not much else that interests him- does he have any other active interests like sports? If not, its definitely unhealthy but there nothing you can do about it. Just watch your life and make your decisions for yourself based on what is acceptable to you and what not.
Try and not get all sentimental- just think of it objectively- what would you tell your sister/closest friend if her boyfriend/husband had such an obsession......would you tell her to tolerate or quit?