This work investigates a multi-product parallel disassembly line balancing problem considering multi-skilled workers. A mathematical model for the parallel disassembly line is established to achieve maximized disassembly profit and minimized workstation cycle time. Based on a product’s AND/OR graph, matrices for task-skill, worker-skill, precedence relationships, and disassembly correlations are developed. A multi-objective discrete chemical reaction optimization algorithm is designed. To enhance solution diversity, improvements are made to four reactions: decomposition, synthesis, intermolecular ineffective collision, and wall invalid collision reaction, completing the evolution of molecular individuals. The established model and improved algorithm are applied to ball pen, flashlight, washing machine, and radio combinations, respectively. Introducing a Collaborative Resource Allocation (CRA) strategy based on a Decomposition-Based Multi-Objective Evolutionary Algorithm, the experimental results are compared with four classical algorithms: MOEA/D, MOEAD-CRA, Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ), and Non-dominated Sorting Genetic Algorithm Ⅲ (NSGA-Ⅲ). This validates the feasibility and superiority of the proposed algorithm in parallel disassembly production lines.