Don't know what you mean by the memory card showing "files".
When I plug in my HD+, at the top of Calibre on the toolbar towards the center, it shows Library, Device and SD Card A. I've configured SD Card A to put the books in "My Files/Books" and the default for the "Send to Device" button sends them to SD Card A. So, when I click a book and click "Send to Device", it sends only the epub file to that folder--nothing else. Since the cover image is inside the epub file, it has no problem showing that on my Nook. (the cover is all I care to have displayed anyway)
When I later connect my Nook back to Calibre, it shows my books I transferred to SD Card A. If yours does not, I'm not sure what to tell you. Maybe it makes a difference which folder you're putting them into.