Two-dimensional (2D) heterostructures composed of transition-metal dichalcogenide atomic layers are the new frontier for novel optoelectronic and photovoltaic device applications. Some key properties that make these materials appealing, yet are not well understood, are ultrafast hole/electron dynamics, interlayer energy transfer and the formation of interlayer hot excitons. Here, we study photoexcited electron/hole dynamics in a representative heterostructure, the MoS2/WSe2 interface, which exhibits type II band alignment. Employing time-dependent density functional theory in the time domain, we observe ultrafast charge dynamics with lifetimes of tens to hundreds of femtoseconds. Most importantly, we report the discovery of an interfacial pathway in 2D heterostructures for the relaxation of photoexcited hot electrons through interlayer hopping, which is significantly faster than intralayer relaxation. This finding is of particular importance for understanding many experimentally observed photoinduced processes, including charge and energy transfer at an ultrafast time scale (<1 ps).