From what I remember, there is handicap parking close to the entrance, so your husband
I came to the Catholic Parenting board to ask about Catholic Homeschooling curriculum and your post caught my eye.
As another poster mentioned, there is handicap parking closer to the Basilica and the Basilica itself is accessible. I would only suggest not only arriving VERY early but getting your seats early as well because it is expected to be very crowded.
If you have any other specific questions though regarding the extent of the handicap accessibility I suggest calling Holy Hill directly. They are extremely friendly and very willing to help and answer questions. My 10 year old called one time with a bunch of questions for a research project. We didn't realize he made the call until he was 35 minutes into the call! So I am sure they wouldn't mind you calling about the extent of their handicap accessibility.