The integration of hybrid alternating current (AC) and direct current (DC) networks has gained relevance due to the growing demand for more flexible, efficient, and reliable electrical systems. A key aspect of this integration is the parallelization of power converters, which presents several technical challenges, such as current sharing imbalances, circulating currents, and control complexity. This paper proposes a distributed control architecture for parallel resonant CLLC dual active bridge (DAB) converters to address these issues in hybrid AC–DC networks and microgrids. The approach includes a master voltage controller to regulate the output voltage and distributed local current controllers to ensure load balance. The approach minimizes the difference between the output and input voltages, allowing for independent control of power flow. Simulation and experimental results show significant improvements. The system stability has been demonstrated experimentally. Transient response has been improved with response time 80% lower using the feed-forward term. The system maintained stability with current sharing deviations below 3% under full and low load conditions. Finally, scalability is ensured by the proposed distributed controller because the central power controller is not affected by the number of units in parallel used in the application. This solution is suitable for advanced hybrid networks and microgrid applications.