In this paper, a Backstepping Global Integral Terminal Sliding Mode Controller (BGITSMC) with the view to enhancing the dynamic stability of a hybrid AC/DC microgrid has been presented. The proposed approach controls the switching signals of the inverter, interlinking the DC-bus with the AC-bus in an AC/DC microgrid for a seamless interface and regulation of the output power of renewable energy sources (Solar Photovoltaic unit, PMSG-based wind farm), and Battery Energy Storage System. The proposed control approach guarantees the dynamic stability of a hybrid AC/DC microgrid by regulating the associated states of the microgrid system to their intended values. The dynamic stability of the microgrid system with the proposed control law has been proved using the Control Lyapunov Function. A simulation analysis was performed on a test hybrid AC/DC microgrid system to demonstrate the performance of the proposed control strategy in terms of maintaining power balance while the system’s operating point changed. Furthermore, the superiority of the proposed approach has been demonstrated by comparing its performance with the existing Sliding Mode Control (SMC) approach for a hybrid AC/DC microgrid.