To mitigate the mismatch between flight schedule demand and airport–airspace capacity during peak periods, this study proposes a collaborative flight scheduling optimization method considering airport–airspace coupling constraints. Airport capacity, waypoint capacity, and minimum turnaround time constraints are incorporated into a multi-objective optimization model, with flight schedule displacement, airline adjustment fairness measured by the Gini coefficient, and total system delay as the objectives. An improved particle swarm optimization algorithm integrating a complex-order Darwinian mechanism and multi-swarm collaboration is developed to enhance search stability and reduce premature convergence. The method is validated using peak-period operational data from the two airports in Chengdu. Results show that the total delay is reduced from 18,532 min to 10,618 min, and the Gini coefficient of airline adjustment amounts is 0.0765, indicating a balanced distribution of adjustment burden among airlines. Airport and waypoint traffic peaks are also smoothed over time. Comparative and ablation experiments further demonstrate that the proposed algorithm outperforms IWPSO, GA, and WOA in convergence quality, solution stability, and sustained optimization capability. The proposed method provides decision support for collaborative flight scheduling and coordinated utilization of terminal-area airspace resources under high-density operations.