Hybrid free-space optical (FSO)/radio-frequency (RF) systems have emerged as a promising solution for high-data-rate wireless backhaul. We present and analyze a switching-based transmission scheme for the hybrid FSO/RF system. Specifically, either the FSO or RF link will be active at a certain time instance, with the FSO link enjoying a higher priority. We considered both a single-threshold case and a dual-threshold case for FSO link operation. Analytical expressions have been obtained for the outage probability, average bit error rate, and ergodic capacity for the resulting system. Numerical examples are presented to compare the performance of the hybrid scheme with the FSO-only scenario.