Power grids are progressing, and the possibility of incorporating DC grids toward hybrid AC/DC grids is gaining increasing relevance, as several technologies available nowadays are operating natively in DC. This paper proposes a topology of a full-controlled bidirectional dual-stage interleaved converter for interfacing hybrid AC/DC grids. The topology is based on a dual-stage architecture, constituted by an AC/DC converter and by a DC/DC converter, both based on interleaved power converters. On the AC side, which is connected to the main AC power grid, the proposed dual-stage architecture operates with sinusoidal current in phase or phase opposition with the voltage, meaning a bidirectional operation. In addition, it has the possibility of interfacing with other AC loads, such as domestic electrical appliances, or with an AC microgrid. The DC link, formed by the AC/DC power stage, is interfaced with a DC power grid, which provides numerous advantages, e.g., for interfacing battery electric vehicles directly charged in DC, as well as other DC loads, such as renewable energy sources. The DC/DC power stage is considered for interfacing with an energy storage system, which is capable of bidirectional power exchange with the DC grid or with the AC grid through the AC/DC power stage. A complete laboratory prototype was designed and developed, with the unified control algorithms implemented on a digital signal processor. The experimental results validated the operation of the full-controlled bidirectional dual-stage interleaved converter based on the specifications for the hybrid AC/DC grid, such as bidirectional operation, synchronization with the AC power grid, predictive current control, interleaved operation on both AC/DC and DC/DC power stages, DC-link voltage control for the DC grid, as well as the operation with different power levels.