This paper presents a secrecy performance analysis of a parallel free-space optical/millimeter-wave (mm-wave) communication system with a selection-combining receiver over a unified Fisher-Snedecor 𝓕-distribution channel. The 𝓕distribution model, with the proper parameters, may be used to describe both the mm-wave and optical channels. The security performance is specifically evaluated by deriving closed-form expressions for the average secrecy capacity, secrecy outage probability, and strictly positive secrecy capacity. We examine the three following distinct security scenarios: 1) An FSO-link eavesdropping attack, 2) mm-wave-link eavesdropping attacks, and 3) eavesdropping attacks on FSO and mm-wave links at the same time. Furthermore, to better understand the influence of various system and channel parameters, asymptotic analysis is performed at high signal-to-noise ratio values. Our developed analytical expressions provide an efficient tool for examining the influence of various system and channel parameters on the secrecy performance, including the atmospheric turbulence severity, pointing errors of the FSO link, fading severity, the shadowing parameters, as well as the number of diversity branches of the mm-wave links. Monte-Carlo simulations are used to verify the correctness of the numerical findings.