It's call a one-penis-policy...so yes, it is a type of Poly relationship. Me, my wife (bisexual), and my girlfriend (straight) have this type of relationship. They both know how I feel and it works for us.
I tried to get over (what some would call jealousy) my issues about having another man in my wife's or my girlfriend's life. I found that I'm cool with every aspect of either of them having a relationship with another male except sex. For me, I told my wife (then fiance') that she may want to end our relationship becuase I knew that I couldn't get over my issue. I even told her that I would rather see her happiest in a poly relationship where she could have more than one man then just happy with me and other female sexual relationship(s). She told me that she didn't think no one could make her happier than I do and since she knew how much it would hurt me, that she was willing to live with that boundary. We were married less than 6 months after that!! (No, it was not the reason we were waiting, just the way it happened)
I meet & starting dating my girlfriend (who never knew about the poly lifestyle) and I started dating about 4 months after our wedding. Once we (all 3) decided to become a family, we had the talk about my (only) boundary. She stated her boundary (no other women except wifey) to which I agreed. Now, we are a happy family!
I told you that because I wanted you to know that there are some poly relationships that work with a one-penis-policy. You just need to make sure that this would be agreeable with your GF. I also would suggest that you try to get over your issues, who knows, maybe it won't be as bad as mine. But if they are, the big question is are you willing to lose your GF over those issues? I was...because it would have made her happiest! I glad I didn't have too...yet!