A novel knee solution-based membrane-inspired evolutionary algorithm (Knee-MOMTMIEA) is proposed to solve multi-objective multi-task optimization problems. The algorithm integrates hierarchical membrane structures with a knee solution-based information transfer mechanism to enable efficient and adaptive knowledge sharing among tasks. By utilizing knee solutions as representative individuals, the approach enhances convergence and solution quality. Comprehensive experiments on the classical MOMTO test suite validate the algorithm’s effectiveness, demonstrating that Knee-MOMTMIEA consistently outperforms state-of-the-art multi-task optimization algorithms. This work represents a significant advancement in integrating membrane computing with evolutionary multitasking, offering an efficient framework for solving MOMTO problems.