This paper adopts a system view of the hybrid digital subscriber line (DSL) long-term evolution (LTE) access network and presents a framework to perform cooperative downstream resource allocation. Such a hybrid network is of particular interest to rural and remote areas served with slow DSL connections not being able to deliver bandwidth-demanding services. The framework addresses practical resource allocation challenges encountered by such hybrid systems, notably on the need to tackle different dynamics of the wireline and wireless channels, and to accommodate subscribers' diverse traffic demands. We introduce the concept of throughput gap (TG), which plays a pivotal role in forging efficient internetwork resource allocation for the hybrid network while facilitating coexistence of legacy DSL modems. Specifically, underutilized LTE resource blocks are opportunistically scheduled as an add-on, on an on-demand basis, to fill the TG of the hybrid modem. Based on this concept, the resource allocation problem is formulated as a system throughput maximization problem, subject to resource availability, TG fulfillment, user admission, transmit power, and physical resource block allocation constraints. We decompose this difficult mixed-integer programming problem into three subproblems that can be solved sequentially. Efficient numerical algorithms are proposed to solve these subproblems, which map to different layers of the LTE protocol stack, and are coupled through signaling exchanges to solve the master problem, resulting in a cross-layer design. Simulation results show that the proposed scheme provides converged network operators a cost-effective alternative to increase the throughput of slow DSL connections when the need arises by leveraging existing LTE infrastructure.