We study the energy dispatch of power distribution networks (PDNs) coupled with urban transportation networks. The electricity demand at each charging/swapping facility is influenced by the arrival rates and charging requests of electric vehicles, which further depends on the spatial distribution of traffic flows over the entire transportation system. We consider the impact of the road congestion on route choices of vehicles from a system-level perspective. The traffic flow pattern in steady state is characterized by the Wardrop user equilibrium. We consider the PDN load perturbation caused by the traffic demand uncertainty, and propose a robust dispatch method that maintains the feasibility of an alternating current power flow constraints. By applying the convex relaxation to nonlinear branch power flow equations, the proposed model yields a two-stage robust convex optimization problem with an implicit uncertainty set. Moreover, a decomposition framework is proposed, in which the first phase determines the uncertainty set of electricity demand by solving two traffic assignment problems associated with the extreme scenarios, and the second phase solves a two-stage robust second-order cone program following a delayed constraint generation framework. Several issues regarding the scalability and conservatism are elaborated. Case studies corroborate the applicability and efficiency of the proposed method.