You can find a demo of possible results below. Note that the card is two-sided. The other side can be seen on hover. I know this doesn't work on iPad and such but I'm fine with that limitation. If someone's really interested, I suppose it's possible to hack up something that works using a bit of JavaScript.
Actual cards can be extracted for printing by first defining a print CSS (missing at the moment) and then exporting the result via web browser (print -> as pdf).
EDIT
It appears it isn't entirely trivial to set up print CSS. Particularly background images are troublesome. I did find out two handy properties: -webkit-print-color-adjust: exact; and content: url(...).
Instead of doing it this way it's probably preferably just to take a screen grab. Since we're using relative measures, we won't have any trouble scaling. Only the images may suffer a bit depending on their original quality.