Can you have a poly relationship without having sex? My husband and I really want a girlfriend but don’t want sexual intercourse.
I mean, sure - the world is a rich tapestry and there probably exists someone who wants to date a couple without having sex with them. But it might be a tough sell for most people.
I'd encourage you and your husband to think about what you really mean when you say "poly relationship" and "girlfriend." What, exactly, do you want? And how would that differ from someone who is a very close friend of you two?
My partner and I have a best friend who my partner has known since he was 14 and I've known since I was 16. We both adore this guy and would go to the ends of the earth for him. He went to high school with my partner and went to college with me. We've all lived together before. We take road trips together. We have each other's backs, we chat frequently, we are emotionally and personally intimate, we are devoted to each other. But my partner and I don't consider him our "boyfriend," nor do we see it as a dating or romantic relationship. It has almost all the hallmarks of one - but not all, so we just let the relationship be what it is and defined the way that works best. Sure, sometimes "friend" feels a little weenie as a term for how much we mean to each other, but we know how our relationship works and what it is, and that matters more.
So consider sitting down and very clearly defining what you want. What kind of intimacy and commitment are you hoping for? And why? What does sexual intercourse or the lack thereof mean to you two? Try to understand your ideal situation. Then, step back and ask yourselves if it's realistic to ask that of another human being.
For example, if you don't want her to have sex with either of you but you want her to be fully committed to you two (not date or have sex with anyone else), realize that's just an inappropriate and completely unrealistic thing to ask or expect.
If you want someone who can strengthen your relationship by just always being there to listen and provide emotional support, who can understand you two deeply and is personally invested in your well-being, look into a couples' counselor - not a girlfriend.
If you want someone who shares your interests and wants to come over a few nights a week to lounge around, play board games, and watch Black Mirror, then maybe you just need a friend. In this case, pitching it as "girlfriend" will actually make it harder, not easier, to find what you're looking for.