In this paper, we study joint rate control, routing and scheduling in multi-channel wireless mesh networks (WMNs), which are traditionally known as transport layer, network layer and MAC layer issues respectively. Our objective is to find a rate allocation along with a flow allocation and a transmission schedule for a set of end-to-end communication sessions such that the network throughput is maximized, which is formally defined as the maximum throughput rate allocation (MRA) problem. As simple throughput maximization may result in a severe bias on rate allocation, we take account of fairness based on a simplified max-min fairness model and the proportional fairness models. We define the max-min guaranteed maximum throughput rate allocation (MMRA) problem and proportional fair rate allocation (PRA) problem. We present efficient linear programming (LP) and convex programming (CP) based schemes to solve these problems. Numerical results show that proportional fair rate allocation schemes achieves a good tradeoff between throughput and fairness.