Two-dimensional (2D) materials and their corresponding van der Waals heterostructures have drawn tremendous interest due to their extraordinary electrical and optoelectronic properties. Insulating 2D hexagonal boron nitride (h-BN) with an atomically smooth surface has been widely used as a passivation layer to improve carrier transport for other 2D materials, especially for Transition Metal Dichalcogenides (TMDCs). However, heat flow at the interface between TMDCs and h-BN, which will play an important role in thermal management of various electronic and optoelectronic devices, is not yet understood. In this paper, for the first time, the interface thermal conductance (G) at the MoS2/h-BN interface is measured by Raman spectroscopy, and the room-temperature value is (17.0 ± 0.4) MW · m-2K-1. For comparison, G between graphene and h-BN is also measured, with a value of (52.2 ± 2.1) MW · m-2K-1. Non-equilibrium Green's function (NEGF) calculations, from which the phonon transmission spectrum can be obtained, show that the lower G at the MoS2/h-BN interface is due to the weaker cross-plane transmission of phonon modes compared to graphene/h-BN. This study demonstrates that the MoS2/h-BN interface limits cross-plane heat dissipation, and thereby could impact the design and applications of 2D devices while considering critical thermal management.