To explore the interface engineering on the carrier recombination in two-dimensional (2D) van der Waals (vdW) heterostructures, we developed a theoretical model to address the size-dependent interlayer and Auger recombination rates in MoS₂/WSe₂ in terms of interface bond relaxation method and Fermi's golden rule. It is found that the Auger recombination lifetime in MoS₂/WSe₂ increases with increasing thickness due to the weakening of Coulomb interaction between holes and electrons, as well as the Auger recombination rate is much smaller than that of MoS₂ and WSe₂ units. However, when the thin h-BN layer is introduced into the MoS₂/WSe₂, the interlayer and Auger recombination rates show opposite trends as the h-BN thickness increases. When the thickness of h-BN reaches 9.1 nm under the condition of 1L MoS₂/h-BN/1L WSe₂, the Auger recombination rate approaches 5.3 ns ^-1. These results indicate that the relevant recombination processes can be tuned by interface and dimension. Therefore, our results provide a useful guidance for the optimal design of 2D transition metal dichalcogenides-based optoelectronic nanodevices.