With the advancement of intelligent manufacturing, flexible job-shop scheduling problems integrating automated guided vehicle (FJSP-AGV) face significant challenges in simultaneously coordinating operation sequencing, machine allocation, and AGV assignment within complex production environments. These environments are characterized by frequent AGV charging requirements due to limited battery capacity, multi-variety and small-batch production patterns, and the need to balance multiple, often conflicting objectives - specially, exit time encompassing both machine processing time and AGV transportation time to the warehouses of all jobs, energy consumption, and machine workload equity. Notably, unplanned AGV charging operations can severely disrupt schedules for both machines and AGV task assignments, resulting in adverse impacts across multiple performance metrics. This underscores the necessity of developing an integrated scheduling approach for FJSP-AGV that explicitly accounts for AGV charging constraints. However, existing research on FJSP-AGV problems largely overlooks the incorporation of AGV charging. To bridge this gap, this study proposes a novel multi-objective integrated optimization model for the FJSP-AGV problem that simultaneously coordinates production scheduling, AGV routing and task assignment, and time- and location-explicit charging decisions. The model simultaneously minimizes exit time, total energy consumption, and maximum machine load. An enhanced NSGA-II algorithm, integrating three improvement strategies, is developed to generate a set of Pareto-optimal scheduling solutions for machines, AGVs, and charging activities. The proposed model and approach are rigorously evaluated on a comprehensive test suite comprising 92 newly generated FJSP-AGV benchmark instances with varying scales and complexity levels, 10 classical FJSP benchmark instances, and a real-world case study from an electronics and electrical equipment manufacturer. Based on rigorous theoretical analysis and empirical validation, evidence-based managerial insights are derived to support decision-making in manufacturing enterprises.