With the development of economic globalization, distributed manufacturing is becoming more and more prevalent. Recently, integrated scheduling of distributed production and assembly has captured much concern. This research studies a distributed flexible job shop scheduling problem with assembly operations. Firstly, a mixed integer programming model is formulated to minimize the maximum completion time. Secondly, a Q-learning-assisted co-evolutionary algorithm is presented to solve the model: (1) Multiple populations are developed to seek required decisions simultaneously; (2) An encoding and decoding method based on problem features is applied to represent individuals; (3) A hybrid approach of heuristic rules and random methods is employed to acquire a high-quality population; (4) Three evolutionary strategies having crossover and mutation methods are adopted to enhance exploration capabilities; (5) Three neighborhood structures based on problem features are constructed, and a Q-learning-based iterative local search method is devised to improve exploitation abilities. The Q-learning approach is applied to intelligently select better neighborhood structures. Finally, a group of instances is constructed to perform comparison experiments. The effectiveness of the Q-learning approach is verified by comparing the developed algorithm with its variant without the Q-learning method. Three renowned meta-heuristic algorithms are used in comparison with the developed algorithm. The comparison results demonstrate that the designed method exhibits better performance in coping with the formulated problem.