To address the stable operation issue of AC/DC hybrid microgrids in islanded mode, a unified droop control strategy based on soft normally open point (SNOP) is proposed. This strategy utilizes a normalization method to combine the frequency droop characteristics of the two feeders with the DC voltage droop characteristics, based on the power balance relationship of the system. The system's operating state is determined by the AC frequency and DC voltage, and SNOP uniformly adjusts the frequency of the AC subgrid and the voltage of the DC subgrid. This ensures that the AC and DC microgrids can evenly share the total power change of the hybrid microgrid, maintaining the AC frequency and DC voltage within the permissible range of the system. Additionally, to prioritize the nearby integration of distributed energy resources and avoid unnecessary actions of SNOP, a deadband adjustment is designed. Then, the AC and DC microgrids can utilize distributed energy resources within each subgrid, thereby reducing the frequent interaction of SNOP on both the AC and DC sides. Finally, the effectiveness of the proposed unified droop control strategy is verified by MATLAB/Simulink simulations.