High-speed rail (HSR) services are experiencing rapid global expansion, posing competition not only in the traditional passenger sector but also challenging air cargo with their attributes of speed and punctuality. In this study, we establish a straightforward model for air-HSR competition in both passenger and cargo markets, taking into account the vertical structure of transportation supply chain. We explore various market equilibria based on the combination of three factors: 1) HSR's provision of cargo services, 2) the integration or separation of HSR's ownership and operation, and 3) uniform or differentiated airport administrative fees for passenger and cargo airlines. The analytical results of our model indicate that the entry of HSR into the cargo market consistently enhances social welfare and may even improve the profit of cargo airlines. However, if airports adopt uniform pricing or there is vertical separation in HSR sector, this could potentially weaken the positive impact on welfare enhancement. These findings have important implications for transportation policy, highlighting how strategic management of infrastructure can significantly influence the effectiveness and societal benefits of HSR's expansion into cargo services.