The energies and dispersions of the image states and quantum well electronic states in layers of Xe and Kr on a Ag(lll) substrate were determined by angle-resolved two-photon photoemission (ARTPPE). For Xe, we measured binding energies of unoccupied electronic states for 1-9 layers and their parallel dispersion out to 4 layers. We measured the binding energies for a monolayer of Kr and dispersions for one and two layers. The n = 2 and n = 3 image states of the bare metal evolve into quantum well states of the layer (states of the Xe conduction band discretized by the boundary conditions of a 2-D slab) at higher Xe thicknesses, where the n = 2,3 states exhibit both a perpendicular and parallel dispersion similar to that of the bulk Xe conduction band. The n = 1 state appears to evolve with coverage as an image state screened by the Xe layer, with appreciable electron density in the vacuum. A continuum dielectric model (modified image state picture) reproduces the gross trends in the data, while an explicit quantum well analysis is used to extract the bulk Xe conduction band dispersion. A simple model which takes into account the band structures of the substrate and the overlayer, as well as the image potential, gives good agreement with the binding energy data. The combination of high energy and momentum resolution along both the surface parallel and surface normal yields very precise measurements of the bulk Xe conduction band as well as information about the behavior of conduction band electrons at interfaces.