In this paper, we present a theoretical discussion of the magnetocaloric effect in the compounds Dy2Cu2Cd and Ho2Cu2Cd whose curves of the heat capacity and isothermal entropy change exhibit two peaks. For this purpose, we use a model Hamiltonian of local magnetic moments with two anisotropic magnetic sublattices. In the model, it is considered that exchange interactions between magnetic moments depend on their xyz components. Besides, it is also included in the model a single ion uniaxial anisotropy and the Dzyaloshinskii-Moriya interaction to account for the canted magnetic moments. Our theoretical calculations show that the existence of these two peaks is associated with a spin reorientation transition at a lower temperature and a ferromagnetic-paramagnetic one at a higher temperature. The results of our theoretical calculations are in reasonable agreement with the existing experimental data of heat capacity and the isothermal entropy change.