In this paper, a dual-hop cooperative satellite-unmanned aerial vehicle (UAV) communication system including a satellite (S), a group of cluster headers (CHs), which are respectively with a group of uniformly distributed UAVs, is considered. Specifically, these CHs serve as aerial decode-and-forward relays to forward the information transmitted by S to UAVs. Moreover, free-space optical (FSO) and radio frequency (RF) technologies are respectively adopted over S-CH and CH-UAV links to exploit FSO's high directivity over long-distance transmission and RF's omnidirectional coverage ability. The positions of the CHs in the 3-dimensional space follow the Matérn hard-core point processes type-II in which each CH can not be closer to any other ones than a predefined distance. Three different cases over CH-UAV links are considered during the performance modeling: interference-free, interference-dominated, and interference-and-noise cases. Then, the coverage performance of S-CH link and the CH-UAV links under three cases is studied and the closed-form analytical expressions of the coverage probability (CP) over both links are derived. Also, the asymptotic expressions for the CP over S-CH link and CH-UAV link in interference-free case are derived. Finally, numerical results are provided to validate our proposed analytical models and thus some meaningful conclusions are achieved.