Two enemies who are sexually involved with each other, but are not allowed to have feelings involved (In theory), as this makes the whole system crash.Enemies by day, sexual enemies by night. They are not allowed to tell anyone either, or go on dates. They do it all indoors and it has to be done by night or in a dark place where they won't be found.
I mean it makes sense for Jason, i dont see him having a girlfriend and a "normal" relationship.
So to this point i only could think of two girls.
Harley Quinn and Huntress.