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The hydrophobicity of an interface determines the magnitude of hydrophobic interactions that drive numerous biological and industrial processes. Chemically heterogeneous interfaces are abundant in these contexts; examples include the surfaces of proteins, functionalized nanomaterials, and polymeric materials. While the hydrophobicity of nonpolar solutes can be predicted and related to the structure of interfacial water molecules, predicting the hydrophobicity of chemically heterogeneous interfaces remains a challenge because of the complex, non-additive contributions to hydrophobicity that depend on the chemical identity and nanoscale spatial arrangements of polar and nonpolar groups. In this work, we utilize atomistic molecular dynamics simulations in conjunction with enhanced sampling and data-centric analysis techniques to quantitatively relate changes in interfacial water structure to the hydration free energy (a thermodynamically well-defined descriptor of hydrophobicity) of chemically heterogeneous interfaces. We analyze a large data set of 58 self-assembled monolayers (SAMs) composed of ligands with nonpolar and polar end groups of different chemical identity (amine, amide, and hydroxyl) in five mole fractions, two spatial patterns, and with scaled partial charges. We find that only five features of interfacial water structure are required to accurately predict hydration free energies. Examination of these features reveals mechanistic insights into the interfacial hydrogen bonding behaviors that distinguish different surface compositions and patterns. This analysis also identifies the probability of highly coordinated water structures as a unique signature of hydrophobicity. These insights provide a physical basis to understand the hydrophobicity of chemically heterogeneous interfaces and connect hydrophobicity to experimentally accessible perturbations of interfacial water structure.