This study proposes an efficient and straightforward hybrid two-level approach for the synthesis of mixed-material heat exchanger networks (HENs). Given the inherently nonlinear and non-convex nature of the governing equations, this methodology employs a genetic algorithm (GA) at the outer level to generate diverse HEN structures. At the inner level, a mathematical optimization model determines the optimal values of continuous variables for each network generated by the algorithm, aiming to minimize the total annual cost (TAC) of the network. This inner-level optimization proceeds in two steps. The first step involves a linear programming model, operating on the principle of maximizing energy recovery, coupled with a search loop to determine stream splitting ratios. The second step implements a linear correction procedure, utilizing the outputs from the first step to identify optimal values for exchanger heat loads, split ratios, and the HEN's minimum approach temperature, thereby improving the likelihood of obtaining a lower TAC. A notable advantage of this approach is, in addition to considering non-isothermal mixing for split streams, the implicit computation of exchanger areas, which permits the consideration of various cost functions for exchangers within the TAC. The results of a case study involving two scenarios showed that the proposed approach reduced the TAC of the network by approximately 0.69% and 0.89% in the first and second scenarios, respectively, compared with the values reported in previous studies.