Electron transfer (ET) at an electrode-electrolyte interface is a crucial step in electrochemical reactions. Computational simulations play an important role in unraveling the effects of the interfacial structure of the electrolyte solution and the applied voltage on the energetics and kinetics. In such simulations, it is important to know the chemical potentials of the electrons in the cathode and the anode and the nonequilibrium response of the interface to the abrupt change in the charge distribution in the system. We have developed a classical fully polarizable molecular dynamics method to deal with the interfacial nonadiabatic ET processes in which both the metal electrodes and the solvent molecules are electronically polarizable. The chemical potential of the electrons in each electrode is introduced based on the chemical potential equalization principle, and their difference between the cathode and the anode is kept equal to the applied voltage. We have investigated the effects of the electronic polarization of the solvent molecules on the interfacial structure of the electrolyte solution and the Marcus free energy curves. The effects are non-negligible for the accurate evaluation of the reorganization energies but become less significant as the redox species comes closer to the electrode surface, where the electronic polarization of the metal electrode plays a more dominant role.