The degradation in magnetic properties in very thin film complex oxides is studied using SrTiO(3)(001)/La(1-x)Sr(x)CoO(3), providing unequivocal evidence for nanoscopic interfacial magnetic phase separation. Electron microscopy and spectroscopy reveal that this occurs due to inhomogeneity in local hole doping, driven by subtle, depthwise variations in the Sr and O stoichiometry. Simple thermodynamic and structural arguments for the origin of these variations are provided.