This paper presents a novel reliability-based multi-material topology optimization framework incorporating coupled geometric nonlinearity, material nonlinearity, and geometric imperfections within a unified Geometrically and Materially Nonlinear Analysis with Imperfections (GMNIA) setting. The bi-directional evolutionary structural optimization (BESO) algorithm is employed as the optimization engine, extended to accommodate multiple candidate materials through a physically consistent constitutive interpolation scheme that ensures admissible material transitions throughout the optimization process. Geometric imperfections are introduced by superimposing scaled linear buckling eigenmodes onto the perfect geometry, simultaneously seeding both local and global instability mechanisms. Reliability constraints are imposed on the available material volume fraction, treated as a normally distributed random variable, such that the reliability index target governs the admissible probabilistic bound on the material resource. Material properties, yield stresses, and geometric imperfection amplitudes are additionally modeled as independent normally distributed random variables, and Monte Carlo simulation is employed to propagate their combined effects through the fully nonlinear structural response at each optimization iteration. A plastic-limit load constraint is incorporated to regulate elasto-plastic behavior by bounding the applied load multiplier below the plastic ultimate load threshold. The proposed framework is validated against two established benchmark problems, namely the MBB beam and the wedge specimen, and subsequently applied to investigate the problem of a U-shaped plate subjected to plastic-limit loading across three load levels. For all three examples, deterministic and reliability-based results are reported across three reliability index targets. The results demonstrate that the proposed framework consistently produces physically meaningful and reliability-calibrated optimal designs, with the material distribution and stress state evolving systematically with the prescribed reliability requirement. The proposed framework represents a significant step toward bridging the gap between advanced nonlinear structural analysis and reliability-based multi-material topology optimization for practical structural engineering applications.