We explore the outcomes of detailed microscopic models by calculating second- and third-harmonic generation from thin-film surfaces with discontinuous free-electron densities. These circumstances can occur in structures consisting of a simple metal mirror, or arrangements composed of either different metals or a metal and a free-electron system like a conducting oxide. Using a hydrodynamic approach we highlight the case of a gold mirror and that of a two-layer system containing indium tin oxide (ITO) and gold. We assume the gold mirror surface is characterized by a free-electron cloud of varying density that spills into the vacuum, which as a result of material dispersion exhibits epsilon-near-zero conditions and local-field enhancement at the surface. For a bilayer consisting of a thin ITO and gold film, if the wave is incident from the ITO side the electromagnetic field is presented with a free-electron discontinuity at the ITO-gold interface, and wavelength-dependent epsilon-near-zero conditions that enhance local fields and conversion efficiencies and determine the surface's emission properties. We evaluate the relative significance of additional nonlinear sources that arise when a free-electron discontinuity is present, and show that harmonic generation can be sensitive to the density of the screening free-electron cloud, and not its thickness. Our findings also suggest the possibility to control surface harmonic generation through surface charge engineering.