What could this mean? Does he want me around for a while?

I'm no love guru but it sounds to me like your boyfriend is comfortable enough in your relationship to kid about you with his parents in front of you. I joke with my mom about my girlfriend with her sitting there implying that things my girlfriend doesn't want me to do "I'm not allowed" and then look at my girlfriend. So I mean from my own experience it sounds like he's vested in your relationship.