The structure of water at interfaces is crucial for processes ranging from photocatalysis to protein folding. Here, we investigate the structure and lattice dynamics of two-layer crystalline ice films grown on a hydrophobic substrate, graphene on Pt(111), with low energy electron diffraction, reflection-absorption infrared spectroscopy, rare-gas adsorption/desorption, and ab initio molecular dynamics. Unlike hexagonal ice, which consists of stacks of puckered hexagonal "bilayers", this new ice polymorph consists of two flat hexagonal sheets of water molecules in which the hexagons in each sheet are stacked directly on top of each other. Such two-layer ices have been predicted for water confined between hydrophobic walls, but not previously observed experimentally. Our results show that the two-layer ice forms even at zero pressure at a single hydrophobic interface by maximizing the number of hydrogen bonds at the expense of adopting a nontetrahedral geometry with weakened hydrogen bonds.