We investigate adaptive transmission schemes over a hybrid radio frequency (RF)/free space optical (FSO) backhaul network for connecting macro-cell base station with small-cell base station through multiple parallel buffer-aided relay nodes. The proposed adaptive transmission schemes improve delay-throughput trade-off of backhaul network by exploiting the degrees-of-freedom over both RF and FSO links and capturing quality-of-service (QoS) requirements. We study two different system configurations, namely, single-carrier and multi-carrier hybrid RF/FSO systems. Our goal is to maximize the constant data arrival rate to the network such that the total queue occupancy in the network is bounded with certain acceptable queue-length bound violation probability. Towards this goal, we formulate novel optimization problems in order to maximize the end-to-end effective capacity over RF and FSO links of both system configurations. Efficient solutions are derived by employing the Lagrangian optimization technique. Some interesting insights are also revealed by considering special cases on link conditions and QoS requirements. Simulation results provide the following two observations: (i) the proposed adaptive transmission scheme outperforms the conventional switch-over hybrid RF/FSO transmission, especially in clear to moderately harsh weather conditions; and (ii) compared to several non-buffer-aided and buffer-aided relaying with non-adaptive transmission schemes, the proposed adaptive transmission scheme substantially improves the supportable data arrival for the hybrid RF/FSO backhaul network.