The islanding operation of hybrid microgrids (HmGs), which adopt the unified interphase power controller (UIPC) as the major element for interconnecting of AC and DC subsystems, is analyzed in this work. The studied HmG includes two AC subsystems and one energy storage-based DC subsystem (ESDC) and some flexible loads. A model reference adaptive control (MRAC) mechanism is suggested to control the UIPC, maintaining an appropriate bidirectional power flow control with simple structure. As another contribution, a new structure topology for the UIPC's power converter at DC side is proposed based on the dual-active-bridge topology and a harmonic-based modeling approach is follow-up for UIPC's power converter modelling. The results of simulations indicate acceptable islanding operation performance of HmG with the proposed structure.