Understanding the electronic coupling and energy flow across layered two-dimensional heterostructures (HSs) is crucial to the exploitation of carrier and phonon transports as well as thermal management in next-generation optoelectronic devices. By using reflection ultrafast electron diffraction, we directly examine photoinduced out-of-plane structural dynamics of supported MoS2/WS2 bilayer HSs and their individual monolayers. Experimental evidence reveals the launch of ultrafast carrier-coupled intralayer atomic motions due to interlayer charge transfer across the van der Waals (vdW) heterojunctions that is absent for individual monolayers. Such a notable carrier-lattice correlation is in addition to the electronic coupling manifested in the enhanced optical absorption for HSs. Also, different pathways of energy flow as a result of carrier-phonon coupling and phonon scattering are reported with the corresponding characteristic times. On longer timescales, relaxation of thermalized atomic motions can be sufficiently described by a thermal transport model. A higher thermal boundary conductance (TBC) across MoS2/WS2 HSs is obtained compared to those at the monolayer-substrate interfaces; however, the similar TBC values suggest comparable couplings of phonons across vdW contacts. These results further shed light on the optical, phonon, and interfacial thermal properties of vertically-stacked vdW HSs.