I'm with you, Del. "Copies" would be confusing. Besides, if it's only a card, I'd put both copies on the same sheet.
A copy of the front side and a copy of the back side.
A copy of both sides. Copies of both sides. Copies of each side.
Use GG's golden rule. Which would be easier for the reader to understand?
I want you to send me a copy of every one of those photos you showed me.
It may not be grammatical, but it's idiomatic (sez me).