To design an efficient and robust integrated heat exchanger configuration, this work develops a multi-material robust topology optimization (RTO) model, and simultaneously considers the distribution of solid, fluid, and metal foam. In the proposed RTO model, the inlet flow velocity and the metal foam porosity are both treated as random variables, while two pseudo-density fields function as design variables. The objective is to maximize both the heat exchange performance mean and thermal robustness, subject to the constraints that the flow dissipation mean ({\mu }_J) and the structural average strain energy mean ({\mu }_C) are less than their thresholds. To solve the RTO model efficiently, polynomial chaos expansion is adopted to propagate random uncertainties from the input variables to the multi-physical response of the heat exchanger. The two-dimensional (2D) multi-material-based RTO results demonstrate that compared with the deterministic topology optimization (DTO) configuration, when {\mu }_J is constrained to 10 and 20 times that of the straight channel configuration, the heat exchange performance mean of the RTO configuration is improved by 13.85% and 18.01%, and the robustness is improved by 29.54% and 29.65%. Notably, the metal foam in the configuration obtained by the RTO is distributed around the flow channels. For the three-dimensional (3D) multi-material-based RTO, with {\mu }_J and {\mu }_C constrained to 0.8 and 1.2 times the corresponding values of the straight multi-channel configuration, the mean performance and robustness are improved by 33.35%-42.54% and 53.71%-59.88%, respectively. Furthermore, compared with the conventional bi-material RTO method, the 3D heat exchanger configuration obtained by the proposed multi-material RTO method possesses superior heat transfer performance mean and enhanced thermal robustness, while achieving lower flow dissipation and reduced average structural strain energy.