The large-scale development of electric vehicles (EVs) has transformed the transportation network into a complex network with random and mixed travel of EVs and gasoline vehicles (GVs), and the distribution network has also been a low-carbon grid with uncertain supply and demand, including the interaction of source-grid-station-storage. In the transportation-distribution coupling system (TDCS), it is urgent to develop a coordinated planning method to meet the spatiotemporal charging needs of EVs and ensure the safe operation of the TDCS. Therefore, based on the real-time energy consumption characteristics of EVs and GVs, a mixed traffic flow assignment model is established to better reflect the influence of GVs on the travel and charging behavior of EVs. Then, a multistage planning model of the transportation network in mixed traffic flow is established. Considering the operational characteristics of energy storage integrated soft open points (E-SOP), and cooperating with source-grid-station-storage, a multistage planning model of the distribution network affected by E-SOP is established. Combining with the physical and flow-power coupling constraints, a coordinated planning model is proposed. Based on the case studies of the Sioux Falls transportation network and IEEE 69-node distribution network coupling system, it is verified that the coordinated planning method can reduce the total planning cost by 7.21% compared to separate planning, and E-SOP can reduce the reactive power output and voltage fluctuation of the system.