The future is plastics, it turns out. Our house, also made in 1967–68, is older than I am, yet still has its original Arborite kitchen and bathroom countertops. It's the future now, and despite over 37 years of hot kitchenware, crayons and markers, spills, bangs, and other wear and tear, even the edges aren't peeling.
Just today, I took a pot of boiling pasta straight from the stove, poured out the contents, and then (perhaps unwisely) set the hot metal directly on the countertop. There's no evidence anything happened. Other than the sixties-era retro-grainy design of the eggshell surface, the melamine could be brand new.