He scattering from Xe monolayers adsorbed onto Ag substrates is studied using a quantum stochastic method. Both the He atom and the surface and bulk modes are treated quantum mechanically using a mean-field partitioning of the quantum Liouville equation. The resulting equations of motion permit the evaluation of the reduced density matrix of the He atom subsystem by averaging over a series of "quantum trajectories." The final reduced density matrix of the atomic subsystem, when projected onto the asymptotic states, provides an accurate estimate of energy transfer processes between the atom and the surface. Our calculations indicate that inelastic energy transfer is enhanced near adsorption resonances due primarily to the increased lifetime of the atom near the surfaces as evidenced by marked deviations from the Debye-Waller thermal attenuation rates.