A multistage hybrid model intended for describing heavy-ion interactions in the energy region of the NICA collider under construction in Dubna is proposed. The model combines the initial, fast, interaction stage described by the model of hadron string dynamics (HSD) and the subsequent evolution that the expanding system formed at the first stage experiences at the second stage and which one treats on the basis of ideal hydrodynamics; after the completion of the second stage, the particles involved may still undergo rescattering (third interaction stage). The model admits three freeze-out scenarios: isochronous, isothermal, and isoenergetic. Generally, the HydHSD hybrid model developed in the present study provides fairly good agreement with available experimental data on proton rapidity spectra. It is shown that, within this hybrid model, the two-humped structure of proton rapidity distributions can be obtained either by increasing the freeze-out temperature and energy density or by more lately going over to the hydrodynamic stage. Although the proposed hybrid model reproduces rapidity spectra of protons, it is unable to describe rapidity distributions of pions, systematically underestimating their yield. It is necessary to refine the model by including viscosity effects at the hydrodynamic stage of evolution of the system and by considering in more detail the third interaction stage.