This article presents one bio-inspired immune optimization approach for linear or nonlinear multi-objective chance-constrained programming with any a prior random vector distribution. Such approach executes in order sample-allocation, evolution and memory update within a run period. In these modules, the first ensures that those high-quality elements can attach large sample sizes in the noisy environment. Thereafter, relying upon one proposed dominance probability model to justify whether one individual is superior to another one; the second attempts to find those diverse and excellent individuals. The last picks up some individuals in the evolving population to update low-quality memory cells in terms of their dominance probabilities. These guarantee that excellent and diverse individuals evolve towards the Pareto front, even if strong noises influence the process of optimization. Comparative and experimental results illustrate that the Monte Carlo simulation and important sampling make the proposed approach expose significantly different characteristics. Namely, the former ensures it a competitive optimizer, but the latter makes it effective only for uni-modal or linear chance-constrained programming. The sensitivity analysis claims that such approach performs well when two sensitive parameters takes values over specific intervals.