A theoretical model for vibrational interactions in the hydrogen bonds in molecular crystals with four molecules forming two centrosymmetric dimers in the unit cell is presented. The model takes into account anharmonic-type couplings between the high-frequency N-H(D) and the low-frequency N...O stretching vibrations in each hydrogen bond, resonance interactions (Davydov coupling) between equivalent hydrogen bonds in each dimer, resonance interdimer interactions within a unit cell, and Fermi resonance between the N-H(D) stretching fundamental and the first overtone of the N-H(D) in-plane bending vibrations. The vibrational Hamiltonian, selection rules, and expressions for the integral properties of an absorption spectrum are derived. The model is used for theoretical simulation of the NH stretching bands of 1-methylthymine and its ND derivative at 300 K. The effect of deuteration is successfully reproduced by our model. Infrared, far-infrared, Raman, and low-frequency Raman spectra of 1-methylthymine and its deuterated derivative have been measured. Experimental geometry and frequencies are compared with the results of density functional theory calculations performed at the B3LYP6-311++G**, B3LYP/cc-pVTZ, B3PW916-311++G**, and B3PW91/cc-pVTZ levels.