With increasing environmental awareness and energy requirement, sustainable manufacturing has attracted growing attention. Meanwhile, distributed manufacturing systems have become emerging due to the development of globalization. This article addresses the energy-aware distributed hybrid flow-shop scheduling (EADHFSP) with minimization of makespan and energy consumption simultaneously. We present a mixed-integer linear programming model and propose a cooperative memetic algorithm (CMA) with a reinforcement learning (RL)-based policy agent. First, an encoding scheme and a reasonable decoding method are designed, considering the tradeoff between two conflicting objectives. Second, two problem-specific heuristics are presented for hybrid initialization to generate diverse solutions. Third, solutions are refined with appropriate improvement operator selected by the RL-based policy agent. Meanwhile, an effective solution selection method based on the decomposition strategy is utilized to balance the convergence and diversity. Fourth, an intensification search with multiple problem-specific operators is incorporated to further enhance the exploitation capability. Moreover, two energy-saving strategies are designed for improving the nondominated solutions. The effect of parameter setting is investigated and extensive numerical tests are carried out. The comparative results demonstrate that the special designs are effective and the CMA is superior to the existing algorithms in solving the EADHFSP.