No spouse here with a bad back... it's me! I have a back/neck injury from my youth and tried out a variety of beds (and other sleeping arrangements!) over the years trying to find the best choice.
What I had to do when I was pregnant was sleep on the floor on a 2" thick memory foam mattress topper - it was the only thing that worked!
Now, I find that very, very firm mattress with a 1" memory foam topper works well (the 2" thick one was too "squishy" over the mattress) - and my husband finds that it's fine for him, too.
I think it depends on what's wrong with your husband's back as to what will work best for him. I do find that the firmer beds have always worked better for me. Oh, and don't forget the pillow! I know that my neck injury makes that more important for me, but having the right pillow can help keep the entire spine aligned right.
I'm not sure that helped any, but I can sympathize and hope you find something that works!