With the increase in carbon emission reduction requirements, electric vehicles and hydrogen fuel cell vehicles have been developed rapidly, which also promotes the emergence of electric-hydrogen integrated charging stations (EHICSs). Since the transmission of hydrogen requires specialized equipment and is generally transported by delivery trailers, this also provides a challenge for optimal scheduling of the distribution network containing multiple EHICSs. To address this issue, an optimal scheduling method of multiple EHICSs considering coordinated centralized and distributed hydrogen production is proposed. Firstly, the EHICS model involving electrolyzer, hydrogen fuel cell, hydrogen storage, energy storage and photovoltaic panels is constructed. Next, a delivery trailer model is built to realize the transport of hydrogen among centralized hydrogen production plants and distributed EHICSs. Then, the distribution network model is established based on the branch flow model, and EHICS and delivery trailer models are integrated into it to form a unified optimization model. The total cost of the distribution network is taken as the objective function to pursue the economic optimality of the whole system. The constructed mixed-integer second-order cone programming problem can be solved accurately by off-the-shelf solvers. The results demonstrate that the proposed coordinated method is more economical than using either centralized or distributed hydrogen production alone, as evidenced by its lowest operation costs. In addition, increasing the number of delivery trailers and allowing hydrogen transport between EHICSs could also reduce operation costs.