With the deep transformation of manufacturing toward green and intelligent production, automated guided vehicles (AGVs) are increasingly used in flexible job shops, and the integrated scheduling of AGVs and machines has become a research hotspot. However, existing studies largely ignore equipment idle time and resource contention caused by battery replacement (swapping) in actual production. To this end, this paper investigates the integrated scheduling problem of machines and AGVs under limited battery resources. A green integrated scheduling model is constructed with the objectives of minimizing makespan and total system energy consumption. To address the resource contention and queueing deadlock arising from the limited number of spare batteries in battery swapping stations, a state-aware dynamic battery swapping and queueing collaborative scheduling strategy is proposed. For the solution algorithm, the non-dominated sorting genetic algorithm II (NSGA-II) is improved by designing a three-segment encoding scheme tailored to the problem, introducing a Tent chaotic map to generate a high-quality initial population,and embedding an adaptive large neighborhood search mechanism to enhance local search capability. Finally,simulation experiments validate the effectiveness of the proposed improvement strategies, and the results show that the improved algorithm is an efficient method for solving this problem.