Whatever works for the couple.
Generally speaking once a relationship has been established for a while it's normal for either person to treat the other for an outing. If you are living together it makes sense to split the rent and utilities. One of the perks to being a "couple" is both people should end being able to do more things for less money because they don't each have to foot the whole bill every time.
Having said that this not worth fighting about. If you want you can set aside money for a major getaway or an all inclusive vacation for the two of you.