The uncertainty and volatility of wind power have led to large-scale wind curtailment during grid connections. The adoption of power-to-hydrogen (P2H) system in a microgrid (MG) can mitigate the renewable curtailment by hydrogen conversion and storage. This paper conducts unified modeling for different types of P2H systems and considers the multi-energy trading in a hydrogen-coupled power market. The proposed bi-level equilibrium model is beneficial to minimize the energy cost of microgrids. Firstly, a microgrid operation model applied to different P2H systems including an alkaline electrolysis cell (AEC), a proton exchange membrane electrolysis cell (PEMEC), or a solid oxide electrolysis cell (SOEC) is proposed at the upper level. Secondly, an electricity market–clearing model and a hydrogen market model are constructed at the lower level. Then, the diagonalization algorithm is adopted to solve the multi-market equilibrium problem. Finally, case studies based on an IEEE 14-bus system are conducted to validate the proposed model, and the results show that the microgrid with a P2H system could gain more profits and help increase the renewable penetration.