Inverter air conditioners (IACs), as one of the most promising demand-side resources, have great potential in improving the frequency performance of islanded microgrids (MGs). This paper proposes a hierarchical control strategy for IACs to provide frequency regulation service while guaranteeing the comfort requirements of users and fair power participation among IACs. The proposed hierarchical control strategy includes a local layer and a supervisory layer. For the local layer, according to the normal-form-based nonlinear control theory, a decentralized controller is designed by using system frequency and indoor temperature signals to improve frequency dynamic performance in the frequency recovery state while guaranteeing comfort requirements. For the supervisory layer, based on the mismatched power of islanded MGs, a consensusbased distributed controller is proposed to provide a shared power adjusting ratio to guarantee fair participation among IACs during the provision of frequency regulation service. A trapezoidlike operating region membership function is introduced to automatically switch the dominant roles of the two controllers to achieve the control objectives of local and supervisory layers. The IEEE 34-bus test system is performed in MATLAB/Simulink platform to confirm the superior performance of the proposed hierarchical control under several scenarios, including different power shortage proportions and continuous critical contingencies. Simulation results showcase that the proposed control strategy can significantly improve frequency performance while guaranteeing user comfort and fair power participation among IACs.