In the actual production, the insertion of new job and machine preventive maintenance (PM) are very common phenomena. Under these situations, a flexible job-shop rescheduling problem (FJRP) with both new job insertion and machine PM is investigated. First, an imperfect PM (IPM) model is established to determine the optimal maintenance plan for each machine, and the optimality is proven. Second, in order to jointly optimize the production scheduling and maintenance planning, a multiobjective optimization model is developed. Third, to deal with this model, an improved nondominated sorting genetic algorithm III with adaptive reference vector (NSGA-III/ARV) is proposed, in which a hybrid initialization method is designed to obtain a high-quality initial population and a critical-path-based local search (LS) mechanism is constructed to accelerate the convergence speed of the algorithm. In the numerical simulation, the effect of parameter setting on the NSGA-III/ARV is investigated by the Taguchi experimental design. After that, the superiority of the improved operators and the overall performance of the proposed algorithm are demonstrated. Next, the comparison of two IPM models is carried out, which verifies the effectiveness of the designed IPM model. Last but not least, we have analyzed the impact of different maintenance effects on both the optimal maintenance decisions and integrated maintenance-production scheduling schemes.