Isotope effects on rate processes and spectra are often used to elucidate the nature of the interactions underlying molecular structure and dynamics. In this paper, we present a computational study of the effect of substituting hydrogen by deuterium in a solvated hydrogen-bonded complex on the rates of the various processes involved in the vibrational relaxation of the hydrogen/deuterium stretch and on the corresponding 1D and 2D infrared spectra. The vibrational relaxation is simulated via the mixed quantum-classical Liouville method, where the proton/deuteron is treated quantum mechanically while the other particles are treated in a classical-like manner. We find that the vibrational relaxation pathway and the rates of the various steps in it are similar for the deuterium and hydrogen stretches. However, we also find that isotope substitution modifies the 1D and 2D spectra of the stretch in a qualitative manner. The differences between the spectra are explained in terms of the narrowing and broadening of the fundamental and overtone transition frequency ranges, respectively, and the smaller transition dipole moments in the case of the deuterium stretch. Our results demonstrate that isotope substitution may have a rather dramatic effect on the infrared spectra of a vibrational mode strongly coupled to its environment even though the rate and pathway of the underlying vibrational relaxation may not be overly sensitive to it.