Using the surface-specific vibrational technique of vibrational sum-frequency generation, we reveal that the double-peaked structure in the vibrational spectrum of hydrogen-bonded interfacial water molecules originates from vibrational coupling between the stretch and bending overtone, rather than from structural effects. This is demonstrated by isotopic dilution experiments, which reveal a smooth transition from two peaks to one peak, as D2O is converted into HDO. Our results show that the water interface is structurally more homogeneous than previously thought.