Free-space optical (FSO) links are considered as a cost-efficient way to fill the backhaul/fronthaul connectivity gap between millimeter wave (mmWave) access networks and optical fiber based central networks. In this paper, we investigate the end-to-end performance of dual-hop mixed FSO/mmWave systems to address this combined use. The FSO link is modeled as a Gamma-Gamma fading channel using both heterodyne detection and indirect modulation/direct detection with pointing error impairments, while the mmWave link experiences the fluctuating two-ray fading. Under the assumption of both amplify-and-forward and decode-and-forward relaying, we derive novel closed-form expressions for the outage probability, average bit error probability (BER), ergodic capacity, effective capacity in terms of bivariate Fox's $H$-functions. Additionally, we discuss the diversity gain and provide other important engineering insights based on the high signal-to-noise-ratio analysis of the outage probability and the average BER. Finally, all our analytical results are verified using Monte Carlo simulations.