This paper presents a comprehensive data-driven distributed combined primary/secondary controller design method for microgrids. This method provides transient and steady-state performance including power-sharing and voltage and frequency restoration while guaranteeing stability for fixed communication delay. The measured data is directly used for controller design with no need for knowledge about the order or structure of the system and grid physical parameters. Moreover, no assumption is made on X/R-ratio of feeders. All the control specifications are formulated as frequency-domain constraints on the 2-norm of weighted sensitivity functions. Then, using a recently developed frequency-domain robust control design method, a distributed fixed-structure controller is synthesized in one step. The performance of the obtained controller is validated using Hardware-In-the-Loop (HIL) experiments. The results show considerable improvement in transient performance, while providing power-sharing and voltage and frequency restoration using distributed implementation.