For anyone to access the grades or financial documents of your child or stepchild- their is a process. It's not as hard as a supeona- it's just a form that you fill out with the college that grants access.
If the college has difficulty with it being his stepfather, then you fill out the form and get the access (it's usually email access) and allow your husband to view the information. This is a pretty common process, so don't worry. Get on the phone with the registrar's office, and ask them for help to get this figured out.
Shirley Cress Dudley, MA LPC NCC FACMPE
Executive Director of The Blended and Step Family Resource Center
Best selling author of the book, Blended Family Advice