I know there are exterior latex paings w/poly in them but I don't know about 'interior paints'. You might want to consult your local Paint Retailer (found in the YELLOW PAGES under PAINT - RETAIL) for more info. That is, of course, unless someone else here doesn't answer your question directly.
Insofaras the bigger picture with your project, you're running the risk of getting paint chips in your food, unless that is, the part of the countertop you're talking about isn't anywhere near your 'working space'. I'm sure you weren't happy w/the original color of the countertops but painting them (in my book) is a health hazard. To each her own.