Remanufacturing, with its environmental and economic implications, is gaining significant traction in the contemporary industry. Owing to the complementarity between remanufacturing process planning and scheduling in actual remanufacturing systems, the integrated remanufacturing process planning and scheduling (IRPPS) model provides researchers and practitioners with a favorable direction to improve the performance of remanufacturing systems. However, a comprehensive exploration of the IRPPS model under uncertainties has remained scant, largely attributable to the high complexity stemming from the intrinsic uncertainties of the remanufacturing environment. To address the above challenge, this study proposes a new IRPPS model that operates under such uncertainties. Specifically, the proposed model utilizes interval numbers to represent the uncertainty of processing time and develops a process planning approach that integrates various failure modes to effectively address the uncertain quality of defective parts during the remanufacturing process. To facilitate the resolution of the proposed model, this study proposes an extended non-dominated sorting genetic algorithm-II with a new multi-dimensional representation scheme, in which, a new self-adaptive strategy, multiple genetic operators, and a new local search strategy are integrated to improve the algorithmic performance. The simulation experiments results demonstrate the superiority of the proposed algorithm over three other baseline multi-objective evolutionary algorithms.