Manufacturing systems are increasingly required to operate in high-mix, low-volume production environments, where process flexibility is crucial. One effective way to achieve this flexibility is through the use of multiple processing alternatives (MPA), allowing a product to be produced using different process plans or component structures. In MPA environments, scheduling decisions must address both the selection of processing alternatives for each product and the execution order of the resulting production tasks. Additionally, processing times often vary due to machine conditions and process variability, further complicating scheduling. This study introduces a dual-network-based deep reinforcement learning method for scheduling in manufacturing systems with multiple processing alternatives. The framework utilizes two Q-networks to learn both the selection of processing alternatives and the dispatching rules. Computational experiments demonstrate that the proposed method effectively reduces both the average makespan and its variability compared to a genetic algorithm-based approach, particularly as the problem size increases, showcasing its effectiveness in the face of processing time uncertainty.