As a novel computing paradigm, multi-access edge computing (MEC) empowers resource-constrained mobile terminals with robust and versatile computational capabilities. However, the development of precise offloading strategies, which determine the execution location for tasks, remains a prominent and unresolved challenge for MEC. The real-life MEC environment is characterized by its non-ideal and uncertain nature. In progressively sophisticated applications, intricate dependency relationships among their tasks continuously intensify. These factors significantly amplify the challenges associated with developing efficient offloading strategies. In this pa per, we study the dependent task offloading problem for MEC under uncertainty with joint consideration of concurrent multi-path transmission, task caching, and privacy protection. Firstly, we employ stochastic numbers to effectively characterize uncertainties and formulate the task offloading problem as a constrained stochastic joint optimization model. We establish an uncertain joint optimization model to formulate the problem of de pendent task offloading in MEC under uncertainty and prove its NP-hardness. The established model focuses on optimizing the joint strategy to achieve the objectives of reducing latency, decreasing energy consumption, and enhancing task utility. Secondly, we decompose the model into two chance-constrained sub-problems and propose a hybrid two-layer offloading algorithm that combines an improved genetic algorithm, Monte Carlo simulation, and artificial neural networks to solve the joint strategy. The proposed algorithm leverages the collaborative synergy between inner and outer layers to solve the joint strategy. The experimental results demonstrate that the established model exhibits significant effectiveness in reducing the objective value, achieving a 34.53% decrease in the objective value compared to local execution. Our offloading algorithm surpasses existing algorithms and attains an average reduction of at least 20.34% in the objective value.