I think going deep is very hard and it requires a lot of trust between you and the therapist. I think it would be hard to do this deep work and revealing if your husband is there. It's hard enough revealing to the T, you don't need to be thinking of how your husband will take it or react, etc. Once you can reveal to the T and get some deep work done, you could always reveal what you choose later to your H.

A possible goal in therapy might be to get to the point of managing your anxiety well enough to go on your own to therapy so you can do the deep work that you want. Can you use CBT methods to cope with your anxiety well enough to see your T alone? Can you ask your T for help on that? I understand you may not be able to solve the anxiety completely with these methods, but if you can manage it well enough to go alone, then perhaps you could explore the deep stuff.

I think all the questions you have raised are important to discuss with your therapist.