Hi,
First, I really really like your hat, especially the huge rhinestone buckle. I cannot tell a great deal from the photos, but my eyes are not what they used to be. It looks to be made of a type of fur felt, one with a long furry nap. These types of long nap felts were made to imitate the look of fur (pelts) and were popular in the very early 1900s and then became popular again in the 1950s through the 1970s. Your hat has a very Edwardian look to it, and I'll bet was inspired by that earlier time, but was made in the 1950s (possibly early 1960s). The buckle on your hat was surely inspired by the antique hats of the Edwardian era, it really looks like a few antique millinery buckles I have. I don't know what you mean when you refer to the interior being unique, can you be more specific? I must be missing something as I only see the reverse side of the felt?
I would not call it a pillbox. The hat does not have an exact style name that comes to mind. Hats can often defy being put inot a specific category, or the names for them change through the years.
But it really is a good one!
Mabley Carew is the department store that sold the hat. Perhaps it was also made in their millinery department, perhaps not.