Hello Lunita, glad you found the group

I hear your difficulty as you suspect your H may have BPD, yet he would not be open to the idea. Of course you would like things to get better -- and it's good to hear that both of you are open to relationship therapy. Skilled therapists do have ways to work with the challenges of BPD without labeling or stigmatizing, so it is possible for things to improve without ever having to label or diagnose.
How has relationship therapy gone so far? Has the therapist given either of you any "homework"?
There is also hope because you have the power to make changes in yourself, that don't require your H to agree or cooperate, that can impact the relational dynamic. While there are no guarantees that he will respond to the changes you make, there is the possibility that he will "follow your lead". A great resource for learning about what it takes to be in a BPD relationship is this section on
When a partner has Borderline Personality Disorder.
Besides you and your H, does anyone else live with you?