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In this paper, we study the problem of resource allocation in multiradio multichannel (MRMC) networks. Specifically, under the consideration of diverse quality-of-service (QoS) requirements, we propose a fair QoS-aware resource-allocation scheme for MRMC networks. In this scheme, channel allocation, multipath routing, link scheduling, and radio assignment are jointly considered. The proposed scheme is obtained by formulating the resource-allocation problem into a cross-layer network utility maximization (NUM) problem, in which resources are allocated to services with proportional fairness. To avoid oscillation among optimal solutions due to the use of multipath routing, we transform the optimization program into an equivalent program by utilizing the proximal optimization algorithm. Then, we obtain the optimal solution of the latter by the decomposition method. Numerical results show that the proposed scheme indeed achieves proportional fairness according to diverse QoS requirements while maximizing utility.