Thin buffer layers for strongly mismatched heteroepitaxy of GaAs and InP on Si were investigated with respect to their structural characteristics in a scanning electron microscope (SEM). A novel technique, which is based on energy-dispersive X-ray spectrometry (EDX), was utilized for thickness measurement. With GaAs thicknesses were determined in the range from several mu m down to 10 nm. Their accuracy was confirmed by mechanical surface tracing of selectively etched steps. The crystal quality of the thin layers was probed by electron-channelling patterns (ECP). We found a dependence on buffer-layer thicknesses which was confirmed by spectroscopic ellipsometry. For thin layers the optical absorption coefficient near the band edge, which is a measure of the density of structural defects in thin layers, showed the smallest deviation from the bulk standard. Furthermore, the buffer-layer quality determined by ECP was correlated with the surface morphology and with the density of twin defects in subsequently grown thick main layers of GaAs and InP, respectively. We conclude that EDX and ECP are powerful methods for the structural characterization of thin buffer layers playing a key role in mismatched heteroepitaxy. Both techniques were performed in a SEM, which is a standard tool in research and development as well as in industrial laboratories.