Hybrid AC-DC microgrid is introduced as the future distribution network to utilise both benefits of alternative and direct currents. In such hybrid microgrid, AC and DC loads, renewable-based distributed generators (DGs), controllable DGs and energy storage systems are connected through separate AC and DC links. An up-down operation model of such hybrid microgrid is proposed which consists of system- and device-level. In the system-level, a mixed integer linear model is suggested to balance the generation and load considering the interconnection of AC and DC subgrids for minimising total operating cost of the system in a 24-hour period. In the device-level, a controller is suggested for power converter-based resources (i.e. intergrid inverter and battery) for controlling the voltage variations in AC and DC subgrids. The effectiveness of the proposed up-down operation model is demonstrated through simulation studies on a test hybrid microgrid.