CuInS2 (CIS) films of a typical thickness of 100 nm have been grown epitaxially on sulphur-terminated Si wafers of (001) and (111) orientation and on single-crystalline CaF2 substrates using three-sourer molecular beam epitaxy (MBE). Epitaxial growth of single-phase CIS was confirmed for stoichiometric and slightly Cu-rich CIS by means of X-ray diffraction (XRD) and Rutherford backscattering (RBS) including channelling. As a typical feature of the epilayers, we found deviations from the cation ordering which is expected for the chalcopyrite lattice. Using transmission electron microscopy (TEM), we determined a Cu-Au-type ordering to dominate on the cation sublattice of stoichiometric CIS grown on Si(001). A photoluminescence (PL) study shows that disorder and structural defects due to the epitaxial growth process lead to electronic states deep in the CIS bandgap and that these states can be successfully removed by postdeposition treatments in hydrogen and air at elevated temperatures up to 400 degrees C. The results shed new Light on the interplay of structural and electronic properties of the CIS compound.