In my experience, the only girl whom I frequented that made a big deal of my (almost) complete lack of jealous was a wildly immature person.
In my opinion not being jealous doesn't mean I don't care about her, it means I trust her and confide in her good sense.
Then of course despite our mature approach both my wife and I have our brief moments of jealousy and/or flaunting each other around, that's normal and we are human beings after all.