Superman:
He bows/kneels, at first because he is facing royalty but then once both got together he began doing it to be playful. He gets smug and proud when people call you two a "power couple". So he loves being with you out in public.
Batman:
This man's personal mission is to just slap you with reality each time and watch your straight back and that fake face royals wear crack a genuine smile or a frown and slouch. When he accomplishes that it makes him smile and feel victorious.
Wonder Woman:
It made her happy as she knew these customs and understood this better than the rest. Though apparently not all align so she still had few things to learn, but she was willing and excited to learn those. If you act very posh/better than the rest it angers her so she will tell you to stop thinking you are above the rest since no one is.
J'onn J'onzz:
He is still so serious even when you two got together. He still addresses you with the proper terms, the expected behaviour, all that stuff. When you are working at your royal duties he tries his best to help you. He shows utmost respect and tries not to do anything in public to avoid silly rumors forming about the royal family.
Flash:
He's dating ROYALTY! First time he saw you, with that posture and beauty; he was head over heels right away! Sometimes he slams against you in a hug but then jumps off and bows so deep almost hits the ground with his head, apologizing with your proper term. If you are being too high and tight it annoys him as you behave as if the common people are less just because they weren't born as lucky as you so he will argue with you about it.
Hawkgirl:
She behaved proper at first but second both got together she dropped that as she's dating you, not your title. She makes show to show you the struggles going on so you can try to do something about it. She gets a proud feeling when she sees you executing your duties proper and well.
Green Lantern:
He doesn't care. Still wonders how the hell he got you, yes, but nothing more than that. When you behave as your title too much when it is just you two he gives you a simple "it's just us" as a way to tell you to drop that as he's not someone you are in a meeting with but your partner. He made sure to show you the poor streets and homeless, asking why the hell the royal family doesn't do anything about this with all the money you have.