Six CdTe thin epifilms were prepared by using molecular beam epitaxy on ion beam cleaned InSb (001) substrates with Tsub temperatures ranging from 25 to 250 °C. Thickness dependent vibrational and structural characteristics are meticulously examined by far-infrared reflectivity (FIR) and high-resolution synchrotron extended x-ray absorption spectroscopy (HR-XAS), respectively. The FIR measured line shapes and optical modes for samples prepared on ion beam cleaned InSb at Tsub ≤ 100 °C revealed abrupt interfaces while noticing segregated Sb atoms and In2Te3-like precipitates at CdTe-InSb interfaces for films grown on ion beam cleaned InSb at Tsub ≥ 230 °C. Our simulated reflectivity results, using a traditional multilayer (ambient/film/substrate) optics methodology, are compared reasonably well with the experimental data. To substantiate the Berreman effect, we have also investigated the transmission and reflectivity spectra of CdTe/InSb epilayers and (CdTe)m/(ZnTe)n/InSb superlattices at oblique incidence (θI = 45°). A clear distinction of the transverse optical (ωTO) phonons in the s-polarization and ωTO and longitudinal optical (ωLO) modes in the p-polarization has established a valuable method of assessing long wavelength optical phonon frequencies in technologically important materials. Comprehensive analysis of HR-XAS results on the structural characteristics of CdTe/InSb epilayers has provided values of bond lengths and coordination numbers in very good agreement with the existing bulk CdTe data.