Proton discharge on metal electrodes, also denoted the Volmer reaction, is a critical step in a wide range of electrochemical processes. This electrochemical proton-coupled electron transfer (PCET) reaction is predominantly electronically adiabatic in aqueous solution and is typically treated as fully adiabatic. Recently, a theoretical model for this PCET reaction was developed to generate the vibronic free energy surfaces as functions of a collective solvent coordinate and the distance of the proton-donating acid from the electrode. Herein a unified formulation is devised to describe such PCET reactions in terms of a curve crossing between two diabatic vibronic states corresponding to the lowest two proton vibrational states, employing an interpolation scheme that spans the adiabatic transition state theory, nonadiabatic Fermi golden rule, and solvent-controlled regimes. In contrast to previous treatments, application of this formulation to the aqueous Volmer reaction highlights the importance of vibrational nonadiabaticity and solvent dynamics. The calculated transfer coefficients and kinetic isotope effects are in reasonable agreement with experimental measurements. These fundamental insights have broad implications for understanding electrochemical processes.