We demonstrate that the hydration repulsion between smooth charged surfaces can be attributed to the interplay of two effects which are not taken into account in the conventional DLVO theory. These are the finite size of the counterions and the variable dielectric permittivity across the electric double layers, We involve these two effects in the theory by coupling the Poisson-Boltzmann equation with the Bikerman and Booth equations, The resulting nonlinear ordinary differential equation of second order is solved numerically, The theory is applied to interpret available experimental data for the dependence of the surface force on the distance measured by means of the surface force apparatus, Excellent agreement between theory and experiment is obtained with reasonable values of the two adjustable parameters : the area per surface charge and the counterion adsorption energy. It turns out that the contribution of the ionic-excluded volume to the hydration force is several times greater than the contribution due to the dielectric saturation, The developed theoretical approach can find application for interpreting data about the interactions in aqueous thin films, colloidal dispersions, and micellar surfactant solutions in the presence of electrolyte at ionic strengths above 1 mM.