The optimal design of multi-material structures combining ductile and quasi-brittle materials is of significant academic and engineering importance. In this design problem, it is crucial to simultaneously consider the yielding and plastic energy absorption of ductile materials, as well as the strain-softening and stiffness degradation of quasi-brittle materials due to damage accumulation. However, applying gradient-based topology optimization to these coupled nonlinear behaviors has historically been challenging. Since gradient-based methods strictly require the differentiability of the evaluated functions, the primary difficulty stems from gradient discontinuities at yield points and softening initiation points in conventional constitutive models. These discontinuities cause numerical instability, often resulting in stagnating at unclear topologies dominated by intermediate densities. To overcome these issues, this study establishes a robust optimization framework by introducing the subloading surface model (Hashiguchi, 1980). While recent studies (Han et al., 2025; Nara et al., 2025) have demonstrated that this model mitigates instabilities in standard elastoplastic topology optimization, this study uniquely extends the framework to address the strain-softening behavior of quasi-brittle materials. Our approach focuses on resolving the gradient singularity at the softening initiation point—analogous to but distinct from the yield point—thereby enabling a unified and smooth sensitivity analysis across both the yield point and the softening initiation point. In this presentation, we detail the formulation and validation of the proposed method. The SIMP-based constitutive laws and sensitivities for both ductile and quasi-brittle phases are formulated based on the subloading surface model. Numerical examples are provided to verify the effectiveness of the proposed approach. A comparison with a conventional method demonstrates that the proposed framework significantly improves convergence stability and successfully derives mechanically rational structures.