Control- and User-Plane Separation (CUPS) and Space Cellular Networks (SCNs) are promising solutions for delivering ubiquitous connectivity and high-traffic wireless services on a global scale. Nevertheless, the potential benefit of CUPS in the separation networks' coverage and data service functions has not been fully leveraged in enabling reliable connectivity. In this paper, we propose a CUPS-enabled Integrated Space-Ground Cellular Network (CUPS-ISGCN). Specifically, Control Base Stations (CBSs) are optimized by deploying them on the space layer to form the Control Plane (CP) and increase coverage for more users over a wide area. Meanwhile, Traffic Base Stations (TBSs) located on the ground layer form the User Plane (UP) and deliver high bit rates within the coverage area of the CP. To maximize CP coverage and improve UP efficiency, we introduce CUPS-enabled SCN into the CP and provide the analytical models to analyze the performance of the CUPS-ISGCN in terms of CP coverage and UP efficiency. By using stochastic geometry, we derive the general closed-form expressions for CP coverage. Then, we thoroughly study UP's performance as a function of the channel parameters between 2-planes, CP and UP. Based on the analysis results, it's proved that the proposed CUPS-ISGCN structure improved the CP coverage performance and UP efficiency.