The interface between water and folded proteins is very complex. Proteins have "patchy" solvent-accessible areas composed of domains of varying hydrophobicity. The textbook understanding is that these domains contribute additively to interfacial properties (Cassie's equation, CE). An ever-growing number of modeling papers question the validity of CE at molecular length scales, but there is no conclusive experiment to support this and no proposed new theoretical framework. Here, we study the wetting of model compounds with patchy surfaces differing solely in patchiness but not in composition. Were CE to be correct, these materials would have had the same solid-liquid work of adhesion (WSL) and time-averaged structure of interfacial water. We find considerable differences in WSL, and sum-frequency generation measurements of the interfacial water structure show distinctively different spectral features. Molecular-dynamics simulations of water on patchy surfaces capture the observed behaviors and point toward significant nonadditivity in water density and average orientation. They show that a description of the molecular arrangement on the surface is needed to predict its wetting properties. We propose a predictive model that considers, for every molecule, the contributions of its first-nearest neighbors as a descriptor to determine the wetting properties of the surface. The model is validated by measurements of WSL in multiple solvents, where large differences are observed for solvents whose effective diameter is smaller than similar to 6 angstrom. The experiments and theoretical model proposed here provide a starting point to develop a comprehensive understanding of complex biological interfaces as well as for the engineering of synthetic ones.