For the frequent occurrence of pulse power load operation and load switching disturbances in AC/DC shipboard microgrids, a large-signal stability analysis method based on hybrid potential theory is proposed. The proposed method utilizes a mixed potential function to analyze the impact of interconnected converters on system stability. First, the entire system is equivalently modeled as a DC system in a d-q rotating reference frame. Then, a mixed potential function model of the AC/DC system is established for stability analysis, leading to the development of a large-signal stability criterion for the system. Using this criterion, the boundary values of bidirectional power transfer for the interconnected converters are derived. Finally, a simulation model of the AC/DC hybrid microgrid system was built in Simulink for verification, and further validation was carried out on the RT-lab hardware-in-the-loop (HIL) simulation platform. Simulation and experimental results show that the proposed criterion can effectively ensure the stability of the AC/DC hybrid microgrid system under large disturbances.