Many photoemission measurements of the valence-band discontinuity are based on the relative positions of the centroids of poorly resolved photoemission peaks. While such measurements are in principle accurate for abrupt, nonreactive interfaces, real interfaces are rarely so simple. We present high-resolution soft x-ray photoemission core level spectra which monitor the band bending and chemistry at two representative heterojunctions. The Si/InP(110) interface is highly reactive, has well-resolved chemically shifted In and P components, and has preferential outdiffusion of In while the Si/GaAs(110) heterojunction has very subtle chemical reactions which are confined to the interfacial region. The effects of even such subtle chemical shifts can obscure the determinations of band bending and lead to errors as large as 0.3 eV for the Si/GaAs(110) heterojunction discontinuity. Such results emphasize the importance of obtaining high-resolution photoemission spectra and applying careful analysis for accurate determinations of band bending and valence-band discontinuities.