To Keep the Laminate, or Not
A laminate counter-top is an acceptable base for ceramic tile, but think carefully before you attempt it. If your counter has curved edges as most do, you'll have to grind off the raised bead at the lip with a belt sander and you won' be able to tile the back splash without cutting off the curved top edge. Some tile stores carry special tiles that will wrap around the front edge, but the selection will be limited. If you choose to go ahead, first rough up the laminate with 100-grit sandpaper, and adhere the tile with an adhesive that's formulated to bond to plastic laminate.
That being said, it is risky to keep the laminate. The grout may crack, and tiles can become loose. Just tear off the old top and use a 3/4-in plywood base and tile backer board.