This paper is concerned with multiobjective evolutionary optimization under uncertainty modeled through probability distributions, with a focus on reliability-based approaches. The contribution is twofold. First, an in-depth study of the notion of probability of dominance is performed, including state-of-the-art multiobjective reliability-based formulations and their numerical calculation. In particular, the notion of dominance limit state function is defined and its properties are thoroughly investigated. Second, the assessment of the probability of dominance is proposed based on a first-order reliability method tailored for Pareto dominance and incorporated into a multiobjective evolutionary algorithm through a repairing mechanism. The analysis of the numerical results on five biobjective benchmark test cases (from two up to five design variables) by means of two adapted metrics (averaged Hausdorff distance and maximum Pareto front error) demonstrates the potential of the proposed approach to reach reliable nondominated fronts within a limited number of generations.