This paper considers a dual-hop cooperative satellite-unmanned aerial vehicle (UAV) communication system including a satellite (S) and a group of cluster headers (CHs) which are respectively with a group of uniformly distributed UAVs. Specifically, the CHs serve as aerial decode-and-forward relays to forward the information transmitted by the S to the UAVs. Moreover, free-space optical (FSO) and radio frequency (RF) technologies are respectively adopted over S-CH and CH-UAV links to exploit the high directivity of FSO over long-distance transmission and the omnidirectional coverage ability of RF. The positions of the CHs in the three-dimensional space follow the Matérn hard-core point processes type-II, in which each CH cannot be closer to another by less 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. Then, the coverage performance of the S-CH link and the CH-UAV link in the aforementioned three cases is studied and the closed-form analytical expressions of the coverage probability (CP) over both two links are derived. Additionally, the asymptotic expressions for the CP over S-CH link and CH-UAV link in the interference-free case are derived. Finally, numerical results are provided to validate our proposed analytical models and thus some meaningful conclusions are achieved.