The distribution of electric fields within the electrochemical double layer depends on both the electrode and electrolyte in complex ways. These fields strongly influence chemical dynamics in the electrode-electrolyte interface but cannot be measured directly with submolecular resolution. We report experimental capacitance measurements for aqueous interfaces of CO-terminated Pt(111). By comparing these measurements with first-principles density functional theory (DFT) calculations, we infer microscopic field distributions and decompose contributions to the inverse capacitance from various spatial regions of the interface. We find that the CO is strongly electronically coupled to the Pt and that most of the interfacial potential difference appears across the gap between the terminating O and water and not across the CO molecule, as previously hypothesized. This "gap capacitance" resulting from hydrophobic termination lowers the overall capacitance of the aqueous Pt-CO interface and makes it less sensitive to electrolyte concentration compared to the bare metal.