Dielectric atomic mirrors are considered in which the repulsive force field owes its existence to an evanescent mode in the presence of a metallic capping layer. The theory of such an atomic mirror is constructed, assuming a finite thickness of the metallic layer with a finite plasma frequency and adopting the field-dipole orientation picture. The Rabi frequency together with the reflectivity for the light incident from within the substrate are evaluated, and their variations with the type of metal and layer thickness analyzed as useful indicators of the effectiveness of the system as an atomic mirror. A number of interesting features are pointed out, including a desirable enhancement. Solutions of the equation of motion for a given atom, subject to given initial conditions, lead to trajectories exhibiting reflection. The leading force fields controlling the dynamics include the average dipole image force plus the average light-induced forces due to the evanescent field. The parameters used to compute the trajectories are similar to those in recent experiments in which Rb atoms incident on a silver film deposited on a glass substrate have been shown to experience enhanced mirror action. The factors controlling the enhancement in general are pointed out and discussed.