Satellite-Terrestrial Hybrid Network (STHN) has become a focus for future communication architecture to accommodate more services and applications. STHN combined with Edge Computing (EC) could provide lower delay, faster transfer speed, and better information transmission. Meanwhile, microservice-based architecture greatly increases system flexibility, which fits the STHN. In this paper, to verify the efficiency of STHN with EC system, we develop a platform based on an open-source EC architecture called KubeEdge. The platform not only helps terrestrial to deploy and manage microservice on satellites but also increases the flexibility of satellite service provision. Besides, in this platform, we design a microservice scheduling algorithm called Optimal Microservice Scheduling with Adaptive Link Changes (OMS-ALC) to minimize communication delay. The experimental results show that OMS-ALC outperforms other solutions in end-to-end delay performance.