It sounds like a silly question, but it's hard to decide.  When I enter the ISBN it comes up as hardcover.  The spine is hard, but the front and back covers are kind of cardboard consistency - stiffer than a typical paperback, but a little flexible (moreso than a hardcover).  The book is The Zen of Zombie (philosophy/humor), and I've seen books of a similar genre with the same kind of cover, but never really thought about whether it is paperback or hardcover.  Any thoughts?

Neither, sounds like a softcover.

It might be what's called a "board book" binding.  Usually that term is reserved for baby books, where the pages are also thick card stock, like the cover.  But I've also seen it used for books where the cover is thick card stock, but the pages are normal paper.

Uf you are unsure whether your book matches the binding then consider listing it "without an ISBN" so it will be assigned a unique number. Because this number is associated only with your book, you could describe the binding as part of the book description.

could it be a turtleback book?  Click here for description

eta:  if so, then I would probably ask the team whether it's okay to post under the ISBN given.

Well, Amazon and Barnes & Noble have it listed only as a paperback, so I guess I will list it without an ISBN and hope one of the 22 wishers finds it.  Thanks for the ideas!

Just don't list it as an "unknown binding" as this doesn't show up for many of the regular search parameters.

Also post it in the bazaar, there are at least two threads that may get it picked up if there are 22 WL'ers.