In this study the processes taking place on the surfaces of nanostructurized Cu/CuO and Cu/CuO/Pd electrodes at different potential, $E$, values in the solutions of 0.1 M KOH in H$_2$O and D$_2$O (heavy water) were probed by the surface enhanced Raman spectroscopy (SERS) and analysis of electrochemical reactions occurring under experimental conditions is presented. Bands of the SERS spectra of Cu/CuO/Pd electrode observed in the range of $E$ values from +0.3~V to 0 V~(SHE) at 1328 - 1569~cm$^{-1}$ are consistent with the existence of species which are adsorbed or weakly bound to the surface with the energy of interaction close to 15 - 21~kJ mol$^{-1}$. These bands can be attributed to the ad(ab)sorbed (H$_3$O$^+$)$\rm{_{ad}}$, (H$_2^+$)$\rm{_{ab}}$ and (H$_2^+$)$\rm{_{ad}}$ ions as intermediates in reversible HER/HOR processes taking place on Cu/CuO/Pd electrode. There was no isotopic effect observed; this is consistent with a dipole nature of electron-ion pair formation of adsorbed (H$_3$O$^+$)$\rm{_{ad}}$ and (H$_2^+$)$\rm{_{ad}}$ or (D$_3$O$^+$)$\rm{_{ad}}$ and (D$_2^+$)$\rm{_{ad}}$. In accordance with literature data SERS bands at 125-146~cm$^{-1}$ and $\sim 520-565$~cm$^{-1}$ were assigned to Cu(I) and Cu(II) oxygen species. These findings corroborate the mechanism of cascading reduction of water.