Angle-resolved photoemission from atomically uniform silver films on iron (100) shows quantum-well states for absolutely determined film thicknesses ranging from 1 to approximately 100 monolayers. These states can be understood in terms of Fabry-Perot modes in an electron interferometer. A quantitative line shape analysis over the entire two orders of magnitude of thickness range yields an accurate measurement of the band structure, quasiparticle lifetime, electron reflectivity, and phase shift. Effects of confinement energy gap, reflection loss, and surface scattering caused by controlled roughness are demonstrated.