Recent studies show that structures based on the traditional "icelike" water bilayer are not stable on flat transition metal surfaces and, instead, more complex wetting layers are formed. Here we show that an ordered bilayer can be formed on a SnPt(111) alloy template and determine the structure of the water layer by low energy electron diffraction. Close agreement is found between experiment and the structure calculated by density functional theory. Corrugation of the alloy surface allows only alternate water molecules to chemisorb, stabilizing the H-down water bilayer by reducing the metal-hydrogen repulsion compared to a flat surface.