My wife and I use the BCP as our shared card for grocery purchases and dining out together (we have semi-independent finances at this point) and it's working out well for us. As Angie55 pointed out, the big box stores that carry a range of goods aren't going to qualify as supermarkets here. I think that the card works best for bigger families that use mainstream supermarkets or other size households that buy "fancy" or "alternative" groceries (organic, local, etc). I can say that our BCP gives 6% on both of the food co-ops that we shop at regularly (as well as the Safeway and Thriftways that we use less often) and that is a big win for us.
If you shop for a lot of groceries at Costco, Sam's Club, etc you may be better off with a store card (e.g., Costco Amex) or a general purpose cash back card like the newer Citi 1%+1% or the 2% Amex from Fidelity (?). Or perhaps that SallieMae MasterCard, if they use a more expansive definition of groceries.