Deep Reinforcement Learning (DRL) has demonstrated promising performance in maintaining safe separation among aircraft. In this work, we focus on a specific engineering application of aircraft separation assurance in structured airspace with high-density air traffic. In spite of the scalable performance, the non-transparent decision-making processes of DRL hinders human users from building trust in such learning-based decision making tool. In order to build a trustworthy DRL-based aircraft separation assurance system, we propose a novel framework to provide stepwise explanations of DRL policies for human users. Based on the different needs of human users, our framework integrates 1) a Soft Decision Tree (SDT) as an online explanation provider to display critical information for human operators in real-time; and 2) a saliency method, Linearly Estimated Gradient (LEG), as an offline explanation tool for certification agencies to conduct more comprehensive verification time or post-event analyses. Corresponding visualization methods are proposed to illustrate the information in the SDT and LEG efficiently: 1) Online explanations are visualized with tree plots and trajectory plots; 2) Offline explanations are visualized with saliency maps and position maps. In the BlueSky air traffic simulator, we evaluate the effectiveness of our framework on case studies with complex airspace route structures. Results show that the proposed framework can provide reasonable explanations of multi-agent sequential decision-making. In addition, for more predictable and trustworthy DRL models, we investigate two specific patterns that DRL policies follow based on similar aircraft locations in the airspace.