The recently presented electrochemical kinetic model, describing the electrochemical hydrogen storage in hydride-forming materials, was extended by the description of the solid/electrolyte interface, i.e., the charge-transfer kinetics and electrical double-layer charging. A complete set of equations was derived, describing the equilibrium hydrogen partial pressure, the equilibrium electrode potential, the exchange current density, and the electrical double-layer capacitance as a function of hydrogen content in both solid-solution and two-phase coexistence regions. The model was applied to simulate isotherms of Pd thin films with nominal thicknesses of 200 and 10 nm. The model demonstrates good agreement between the simulation results and experimental data.