Vibrational spectra of two kaolinite-dimethylsulfoxide intercalates, obtained using inelastic neutron scattering (INS), were analyzed with a view to understanding the dynamics of the hydrogen atoms in the structure. The main focus was on the spectral region 0–1700 cm−1, which is difficult to analyze using optical spectroscopy. The experimental vibrational spectra of kaolinite:dimethylsulfoxide and kaolinite:d6-dimethylsulfoxide collected using two different spectrometers were interpreted by means of the solid-state DFT calculations. Calculated spectra were obtained by both normal-mode analysis and molecular dynamics going beyond the harmonic approximation. The Al–O–H bending modes were found to be spread over the large interval 100–1200 cm−1, with the dominant contributions located between 800 and 1200 cm−1. The shape of the individual hydrogen spectrum depends on whether or not the respective hydrogen atom is involved in an O–H···O hydrogen bond and on its strength. The modes corresponding to the in-plane movements of the inner-surface hydrogen atoms are well defined and always appear at the top of the intervals of energy transfer. In contrast, the modes generated by the out-of-plane movements of the hydrogen atoms are spread over large energy intervals extending down to the region of external (lattice) modes. The C–H modes are concentrated mainly in the three regions 1200–1450 cm−1, 800–1100 cm−1, and 0–400 cm−1. While the first two regions are typical of the various deformational modes of methyl groups, the low-energy region is populated by the modes corresponding to the movements of the whole dimethylsulfoxide molecule.