Sounds pretty immature - but also that your mind is set. you don't specify whether or not she has been around before you got together, or afterwards - aka cheating.
Sounds like a wonderful arrangement o_0 . Do you plan on sticking with her? cheating is never the way. cheating destroys any relationship. you'll have to lie to her, start hiding things. A relationship IS NOT healthy unless it's built on trust. Why do you care if she's been around? Many people have a history, lots of people don't. I've heard many people who wish they could have only one person in their sexual history - their significant other.