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Existing network planning models for electric vehicle (EV) services usually treat the battery swap and the on-board supercharging as two independent processes. This study makes an early attempt to design an EV charging network where battery swap and supercharging are jointly coordinated. The swap and supercharge processes are characterized by Erlang B and Erlang C priority queues, respectively. A strategic location-allocation model is formulated to optimize the station sites, battery stock level, and the number of superchargers at chosen sites. Three design criteria, namely, battery state-of-charge, maximum service time, and power grid constraint, are simultaneously taken into account. Meta-heuristics algorithms incorporating Tabu search are developed to tackle the proposed non-linear mixed integer optimization model. Computational results on randomly generated instances show that the priority battery service scheme outperforms the pure battery swap station in terms of spare battery investment cost and charging flexibility. The case study on a real-world traffic network comprised of 0.714 million households further shows the efficacy and advantage of the dual battery charging process for ensuring state-of-charge, service time commitment, and network-wide grid stability.