The potential of renewable energy should be fully exploited in the transportation sector to achieve a cleaner production. Therefore, this paper proposes an on-grid hybrid hydrogen refueling and battery swapping station powered by wind energy. This novel concept can promote the development of low-carbon emission vehicles including hydrogen-based vehicle and battery electric vehicle. During the daily operation of the station, the multiple uncertainties may lead to a higher operational cost. To address this problem, a hybrid stochastic/distributionally robust optimization method is proposed to handle different uncertainties for the energy management problem. The first type of uncertainties can be depicted by a certain distribution, i.e. electricity price and wind power, which is processed by a stochastic optimization method. The second type of uncertainties is associated with human behaviors and is difficult to find its probability distribution, i.e. the hydrogen demand of hydrogen-based vehicles, so the second type is processed by a distributionally robust optimization method. The overall objective is to minimize the total operational cost of the station, which also considers the battery swapping station overstock punishment. Because a reasonable battery swapping scheduling can reduce the waiting time of users and operational cost of the station. The results indicate that the proposed method can effectively address the conservatism of solutions as its total operational cost is 4.4% lower than that of the hybrid stochastic/robust optimization method under a high confidence level.