Electronic and vibrational states in CdTe/ZnTe quantum dot multilayers grown on a thick ZnTe buffer layer are studied using optical spectroscopy methods (photoluminescence in a wide temperature range, Raman scattering, and IR reflection). It has been established that a new band appears in the Raman spectra of sample with a small ZnTe spacer layer thickness, which can be ascribed to a vibrational mode of two closely-spaced quantum dots. A comparison of results obtained under studies of structures grown on ZnTe and CdTe buffer layers shows that change of strain distribution pattern substantially modifies electron and optical spectra of QD structures. In particular, it can result in change of the band diagram type. A reason of anomalous peak position shift of quantum dot emission band is discussed.