We investigate the potential effects of electric vehicles (EVs) on reducing the load shedding in heavily loaded distribution systems (DSs). Given proper incentives, a considerable number of EVs could provide vital support to holding the load and improving operating flexibility. We propose a network equilibrium model that integrates market clearing in DSs and traffic flow balance in transportation systems. This model captures the decentralized interactions between key stakeholders in transportation and distribution networks as well as the spatial distribution of EV traffic in response to endogenously determined incentive signals. To mitigate the computational challenges brought by the non-convex network equilibrium model, we develop an equivalent convex reformulation with guaranteed global convergence. Numerical studies are conducted to demonstrate the effectiveness of the proposed model and computational performance. The proposed method could provide a fundamental tool for analyzing interdependent transportation and distribution networks coupled by charging facilities and EVs.