Really good advice. Is gay relationship real? Does he share similar values? Beware of spending every waking hour with each other. Are you ready?
Did your husband share with you that he swings both ways?
Your values should be validated by your behavior. Explain that you want to be with her, and that moving in is important to you in the longer term, but that you want some more time to explore and enjoy those elements that only come from living apart. Generally speaking, men are a competitive bunch. Although we are both doing the same thing, its good to grasp a perspective of this.
Opening up the relationship too fast.