The widespread adoption of electric vehicles (EVs) and hydrogen fuel cell electric vehicles (HVs) is tightening the interdependence between power and transportation systems, calling for better coordination between them. To address this challenge, this paper proposed a distributed coordination method for the hydrogen-integrated microgrids and transportation system. First, we introduce energy sharing among microgrids which reduces the overall system cost by 16.2% and analyze how it improves the traffic flow. Additionally, we develop bidding models for microgrids participating in joint energy and ancillary service markets, maximizing flexible resources utilization and increasing revenue by 147%. A mixed vehicle flow transportation system model is then established, including EVs, HVs, and gasoline vehicles. To coordinate the two individual systems efficiently, a distributed algorithm is proposed, incorporating a filtering mechanism that reduces the communication burden by 63% during the iterative process. Uncertainties and nonlinearities are handled using distributionally robust method and linearization techniques. Finally, case studies validate the effectiveness of the proposed method and highlight the mutual impact between the two systems.