In my NJ home we had a counter and sink of solid laminate and I think that may be what you have, as i've seen them in some friends homes here. They can be cleaned with a mild household cleaner and baking soda.
They can get deep scratches in them from pots and pans, so be cautious when washing them. You can sand the scratches out, but it's an awful mess of dust, even with a wet sander.
Here's a link to explain the cleaning that I've located that seems right on the money.
http://www.countertop.com/care/