poppet31 I guess we are all different. It's good people have replied and showed that they also can understand your husband's position.
For me, I never found talking about myself difficult or demeaning. I found the process quite enjoyable and pleasant. I would find your husband's attitude hard to face. But at the end of the day the process does end. For us it was less then two years from start to finish and we are now 5 years down the line and the process is a distant memory!
Focus on the end of the process, having a child come and live with you and parenting them for the rest of your lives.
I've got several negative people in my life and it drives me mad, but then I guess my relentless positivity probably drives them mad too!
"...he just keeps going on about how humiliating it is for him having to sit in front of a panel of people who will know everything about him."
For me, this is a very odd way of looking at life. When I see my doctor she knows all about my life, my biology, my eating problems, my blood pressure, everything. I do not find this at all humiliating, I feel reassured that she knows all this and is trying to help me.
The panel are trying to help you and your husband to bring home a child, they are doing the work for you but also for the child, to ensure that she or he has the best possible chance of overcoming the early difficulties of life and growing up healthy and happy.
Good luck, I hope your husband will come to see this is a very small part of being a parent, and, honestly, this is nothing compared to the challenges of actually raising a child/children.
Good luck and I do wish you all the best. 