We consider joint congestion control and multiuser scheduling in a hybrid wireline and wireless network, where the air interface of wireless links is based on orthogonal frequency division multiplexing (OFDM). For static channels, we formulate this cross-layer design as a network utility maximization (NUM) problem with both wireline and wireless link constraints. The convexity of the problem enables a well-established dual-based approach to decompose it into two subproblems, the transport layer source rate adaptation and the medium access control (MAC) layer multiuser OFDM scheduling, which are connected and coordinated by link prices. While the rate and link price adjustments follow the same fashion as the conventional utility-based congestion control for wireline networks, the key difference is the multiuser OFDM scheduling performed at the wireless access point (AP). Independent from specific utilities used by each source, this scheduling problem always maximizes a wireless linkprice-weighted sum throughput (LPWST), which can be solved efficiently by a block-coordinate descent method, resulting in optimal subcarrier assignment and power allocation at the AP. Convergence of the dual-based algorithm is established using the convex optimization theory. To extend our results to dynamic wireless channels, we provide a NUM formulation with long-term average feasible rate region and develop a gradient scheduling algorithm to handle channel variations. Our work represents a systematic cross-design framework for distributed fair resource allocation in a hybrid network with both static and dynamic wireless channels.