Tree-based Long-Reach Ethernet Passive Optical Networks (LR-EPONs) have become the potential broadband access technologies due to the cost-effectiveness for reducing the expenditure cost and simplifying the Metropolitan Area Network (MAN) and Local Area Network (LAN) architectures. However, the increased propagation delay of LR-EPON leads to a significant increasing for packet delay time, which may dramatically degrade the whole network performance. On the other hand, since the upstream and downstream signal transmissions can take place only along the path between the Optical Line Terminal (OLT) and the Optical Network Units (ONUs), LR-EPONs are unable to support the point-to-point transmission requirements of emerging Peer-to-Peer (P2P) applications. Accordingly, the present study develops a novel network architecture, designated as Tree/RINg LR-EPON (TRINPON), to facilitate private transmissions (i.e., ONU-to-ONU transmissions) among the ONUs in the network. An effective Hybrid Dynamic Bandwidth Allocation (HDBA) mechanism is proposed to support the transmissions between the OLT and the ONUs and also to minimize the end-to-end delays of the private data traffic. The effectiveness and efficiency of the proposed TRINPON architecture and HDBA scheduling scheme are demonstrated by means of numerical simulations.