In an integrated fiber and wireless (FiWi) access network consisting of a wireless subnetwork and an optical subnetwork, multipath routing may be applied in the wireless subnetwork to improve throughput. Due to different delays along multiple paths, packets may arrive at the destination out of order, which may cause Transmission Control Protocl (TCP) performance degradation. In this paper, we propose two mechanisms to improve in-order departure of packets from the optical line terminal (OLT) in a FiWi network and enhance the TCP performance. We first propose an effective scheduling algorithm at the OLT to ensure possible in-order packet arrivals at the destination. We then design a dynamic bandwidth allocation (DBA) scheme in the optical subnetwork (i.e., an Ethernet passive optical network) that gives higher priorities to flows that may trigger fast retransmit and fast recovery in upstream bandwidth allocation. Simulation results show that both the proposed scheduling algorithm and the DBA scheme are effective in improving the TCP performance.