The limited adjustable margin of the islanded AC/DC hybrid microgrid makes it difficult to both balance economic and stability. Therefore, an energy management strategy that can effectively harmonize economic and stability is highly desirable. In view of the issues, this paper proposes a novel dual mode coupling energy management strategy for islanded AC/DC hybrid microgrid. The strategy sets two modes for energy management of islanded AC/DC hybrid microgrid: economic mode and emergency mode. A two-stage stochastic predictive control (SPC) dispatch model is carried out for economic operation in economic mode. Furthermore, the economic mode can be switched to emergency mode according to the SOC (state of charge) of the V/F(voltage/frequency) control unit to ensure the stability of the microgrid. The economic mode is designed to guarantee the economic efficiency during normal operation. In contrast, the emergency mode serves to ensure the stability of the microgrid when the adjustable margin is inadequate. The two operation modes are coupled and closely coordinated. Finally, the strategy is applied in an existent AC/DC hybrid microgrid for experiments. According to the experimental results, this energy management strategy can achieve normal economic operation and short-term risk management of AC/DC hybrid microgrid. Moreover, unlike simulation research, this paper employs actual microgrids for strategy verification. The results demonstrate that the proposed strategy is a comprehensive optimal energy management strategy that can be directly applied to actual islanded AC/DC hybrid microgrid. This represents another major highlight of this paper, alongside the novel strategy itself.