In this paper, we investigate the impact of hardware impairments (HWIs) on the performance of hybrid satellite–aerial–terrestrial networks (HSATNs). The considered network comprises a single satellite, multiple full-duplex (FD) aerial base stations (ABSs), and a ground user, enabling rapid deployment in scenarios such as disaster recovery and emergency communications. The system operates over millimeter-wave (mmWave) bands and employs adaptive antenna structures at the ABSs. To enhance data transmission, we utilize an opportunistic selection scheme for the aerial base stations. We analyze the outage probability and average capacity of the proposed network with HWIs in both the transmitter and receiver chains. Numerical results illustrate the impact of system parameters on perfor mance. Specifically, reducing receiver HWIs improves performance, though the improvement diminishes as self-interference increases. Furthermore, directional antennas and adaptive antenna structures (AS) significantly enhance performance, with AS outperforming fixed structures (FS). Finally, the system is shown to be more sensitive to transmit HWIs than to receiver HWIs, suggesting that transmitter hardware requires more precise design. In contrast, receiver hardware can be chosen from more cost effective components.