Experiments at the LANL Trident facility demonstrated the production of monoenergetic ion beams from the interaction of an ultraintense laser with a target comprising a heavy ion substrate and thin layer of light ions. An analytic model is obtained that predicts how the mean energy and quality of monoenergetic ion beams and the energy of substrate ions vary with substrate material and light-ion layer composition and thickness. Dimensionless parameters controlling the dynamics are derived and the model is validated with particle-in-cell simulations and experimental data.