This paper presents a proposal to charge and discharge valve-regulated lead-acid (VRLA) battery arrays integrated into microgrids by using the bidirectional Cûk converter with a multi-mode multi-loop control scheme based on sliding-mode control. The proposed control integrates the constant current - constant voltage - constant voltage charge method (CC-CV-CV) which is implemented using an inner current loop based on the sliding mode control of the input current of the converter and two nested outer loops based on the voltage and current of the battery. Conversely, the discharge is studied using two operational modes, one using a current reference given by a high level on a hierarchical structure and other using a current reference given by an outer Proportional-Integral (PI) controller regulating the voltage of the DC bus. The modelling of the bidirectional Cûk converter in these applications and its operational modes besides the analysis of the inner loop and the design criteria used in the synthesis of the outer loops are addressed. Simulation results are presented validating the control proposal.