Protein function is executed at the molecular surface, where shape and chemistry act together to govern interaction. Yet most comparison methods treat these aspects separately, privileging either global fold or local descriptors and missing their coupled organization. Here we introduce IFACE (Intrinsic Field--Aligned Coupled Embedding), a correspondence-based framework that aligns protein surfaces through probabilistic coupling of intrinsic geometry with spatially distributed chemical fields. From this alignment, we derive a joint geometric-chemical distance that integrates structural and physicochemical discrepancies within a single formulation. Across diverse proteins, this distance separates conformational variability from true structural divergence more effectively than fold-based similarity measures. Applied to the cytochrome P450 family, it reveals coherent family-level organization and identifies conserved buried catalytic pockets despite the complex topology. By linking interpretable surface correspondences with a unified distance, IFACE establishes a principled basis for comparing protein interfaces and detecting functionally related interaction patches across proteins.