This paper studies the performance of multi-hop and mesh networks composed of millimeter wave (MMW)-based radio frequency (RF) and free-space optical (FSO) links. The results are obtained in cases with and without hybrid automatic repeat request (HARQ). Taking the MMW characteristics of the RF links into account, we derive closed-form expressions for the networks' outage probability and ergodic achievable rates. We also evaluate the effect of various parameters such as power amplifiers efficiency, number of antennas as well as different coherence times of the RF and the FSO links on the system performance. Finally, we determine the minimum number of the transmit antennas in the RF link such that the same rate is supported in the RF- and the FSO-based hops. The results show the efficiency of the RF-FSO setups in different conditions. Moreover, HARQ can effectively improve the outage probability/energy efficiency, and compensate for the effect of hardware impairments in RF-FSO networks. For common parameter settings of the RF-FSO dual-hop networks, outage probability of 10^{-4} and code rate of 3 nats-per-channel-use, the implementation of HARQ with a maximum of 2 and 3 retransmissions reduces the required power, compared to cases with open-loop communication, by 13 and 17 dB, respectively.