Two-dimensional transition metal dichalcogenides (TMDs) and their van der Waals (vdW) heterostructures present a compelling platform for advanced electronic and optoelectronic applications, leveraging their unique quantum confinement and strong light-matter interaction properties. The performance of such devices is fundamentally governed by interface charge transfer dynamics. While recent experiments demonstrate that inserting insulating layers can effectively modulate these dynamics, a predictive theoretical model quantifying how an intercalated insulator influences charge tunneling probabilities remains absent. Moreover, the mechanistic details of how layer-thickness variations tune the potential barriers height and width to regulate charge transfer are not fully resolved. Here, we establish a theoretical framework, combining atomic-bond-relaxation theory with the quantum tunneling model, to systematically investigate how an h-BN dictates the interlayer barrier landscape and tunneling probabilities in WS₂/h-BN/MoS₂ heterostructures. We find that increasing h-BN thickness, which shifts its conduction band minimum downward and valence band maximum upward, reduces the heterostructures barrier height while increasing its effective width. Surprisingly, for a fixed h-BN thickness, the barrier height in a WS₂/h-BN/MoS₂ stack increases with the thickness of either TMD constituent, yet remains lower than that of monolayer-WS₂/h-BN/monolayer-MoS₂ heterostructure with the same h-BN thickness. This elevated barrier in the monolayer configuration is traced to the large exciton binding energies of monolayer WS₂ and MoS₂. Further analysis reveals that when h-BN thickness is held constant, charge tunneling probabilities for electrons and holes are primarily controlled by barrier height and display a non-monotonic dependence on TMD thickness, initially rising then falling. The decline in the monolayer-WS₂/h-BN/monolayer-MoS₂ case is linked to the heightened barrier from strong excitonic effects. In contrast, with TMD thickness fixed, tunneling probabilities decay sharply and exponentially as h-BN thickness grows, with extracted attenuation constants of 0.77 Å^-1 for electrons and 0.74 Å^-1 for holes, a direct consequence of the widening tunnel barrier suppressing coherent interlayer transport. Our results provide a foundational model for understanding and engineering charge transfer dynamics via inserting insulating layers in vdW heterostructures, offering critical insight for the design of tailored optoelectronic interfaces.