This paper addresses the transportation network design problem (NDP) wherein the distance limit and en-route recharge of electric vehicles are taken into account. Specifically, in this work, the network design problem aims to select the optimal planning policy from a set of infrastructure design scenarios considering both road expansions and charging station allocations under a specified construction budget. The user-equilibrium mixed-vehicular traffic assignment problem with en-route recharge (MVTAP-ER) is formulated into a novel convex optimization model and extended to a newly developed bi-level program of the aggregated NDP integrating recharge facility allocation (NDP-RFA). In the algorithmic framework, a convex optimization technique and a tailored GA are adopted for, respectively, solving the subproblem MVTAP-ER and the primal problem NDP-RFA. Systematic experiments are conducted to test the efficacy of the proposed approaches. The results highlight the impacts of distance limits and budget levels on the project selection and evaluation, and the benefits of considering both road improvement policy and recharge service provision as compared to accounting for the latter only. The results also report that the two design objectives, to respectively minimize the total system travel time and vehicle miles travelled, are conflicting for certain scenarios.