Who needs this kind of relationship? If you're in doubt as to whether or not YOU need this here's what I'd do:
Create situations where your girlfriend will go absolutely crazy with jealousy -- mysterious phone calls, notes left in pockets, credit card receipts for 2 espressos....you get the idea, right?
Then, stand back and watch the fireworks as you respond blandly that you have NO idea how those panties got under the bed! Really, NO idea!
Enjoy the drama. It'll either make or break your relationship, and whatever happens is what is suppose to happen. Ride the ride, man!