I think it's part of trusting your T. She made this decision to not talk about her husband for a reason, and it has to be accepted. It's not about shutting you out, it's about keeping his information protected. This part really isn't about you, but about her, about him.

There is also the knowledge that there's been a lot of transference and intense feelings towards T. So if she starts talking about H, what does that open? Then it becomes all about T and T's life. And if she talks about H, even something positive ("My H bought me flowers today") then it runs the risk of "HER H buys her flowers, my H can't do that, or I want to do that for T but she won't let me, etc".

I have to think right now it feels so "messy" with T, and such big, big feelings to get worked out. She's protecting her H, but maybe you too? From opening that door of it being more about her, her husband, her life, what she has, etc?