Epitaxial ${\mathrm{CaF}}_{2}$ and ${\mathrm{SrF}}_{2}$ layers were prepared by molecular-beam epitaxy onto clean, (4\ifmmode\times\else\texttimes\fi{}2)-reconstructed InP(001) surfaces. The geometric and electronic structures of the layers and the interfaces were investigated by low-energy electron diffraction (LEED), Auger-electron spectroscopy (AES), and x-ray and ultraviolet photoelectron spectroscopies (XPS,UPS). Both fluorides grow at the substrate in a (001) orientation in their bulk cubic structures and form atomically rough, (111)-faceted surfaces as deduced from LEED. The XPS core-level intensity attenuations and the AES depth profiles indicate the formation of sharp interfaces. No interface bonds between InP and overlayer atoms were observed with photoelectron spectroscopy, and the Fermi-level position at the InP surface does not shift after fluoride deposition. The core levels and valence-band maxima of the fluoride overlayers shift to higher binding energies with increasing thickness. Up to 0.5-nm coverage, this is explained by additional screening from the InP substrate. Above 0.5-nm coverage, the shifts are caused by electrostatic-potential differences extending 10 nm away from the interfaces into the fluoride overlayers. The potential differences decrease the binding energies of all electronic levels in the fluoride layers near the interfaces, analogous to a band bending in semiconductors at semiconductor surfaces or semiconductor-metal interfaces. These potential differences are generated by mobile ionic defects in the fluoride layers. A model is presented for this space-charge region caused by ionic point defects in insulating overlayers. Fluoride ions are chemisorbed at the InP surface, thus creating a negative interface charge, which is compensated by excess positively charged fluoride vacancies in the space-charge region. The analogy to space-charge regions in semiconductors due to electronic surface states is discussed. Furthermore, the electronic interface schemes with the band discontinuities, the work functions, and the electron affinities of thick ${\mathrm{CaF}}_{2}$ and ${\mathrm{SrF}}_{2}$ overlayers were deduced from the measurements.