The structure and properties of water at biological interfaces differ drastically from bulk due to effects including confinement and the presence of complicated charge distributions. This non-bulk-like behavior generally arises from water frustration, wherein all favorable interactions among water molecules cannot be simultaneously satisfied. While the frustration of interfacial water is ubiquitous in the cell, the role this frustration plays in mediating biophysical processes like protein folding is not well understood. To investigate the impact of frustration at interfaces, we here derive a general field theoretic model for the interaction of bulk and disordered vector fields at an embedded surface. We calculate thermodynamic and correlation functions for the model in two and three dimensions, and we compare our results to Monte Carlo simulations of lattice system analogs. In our analysis, we see that field-field cross correlations near the interface in the model give rise to a loss in entropy like that seen in glassy systems. We conclude by assessing our theory's utility as a coarse-grained model for water at polar biological interfaces.