This paper studies the joint design of routing and resource allocation algorithms in cognitive radio based wireless mesh networks. The mesh nodes utilize cognitive overlay mode to share the spectrum with primary users. Prior to each transmission, mesh nodes sense the wireless medium to identify available spectrum resources. Depending on the primary user activities and traffic characteristics, the available spectrum resources will vary between mesh transmission attempts, posing a challenge that the routing and resource allocation algorithms have to deal with to guarantee timely delivery of the network traffic. To capture the channel availability dynamics, the system is analyzed from a queuing theory perspective, and the joint routing and resource allocation problem is formulated as a non-linear integer programming problem. The objective is to minimize the aggregate end-to-end delay of all the network flows. A distributed solution scheme is developed based on the Lagrangian dual problem. Numerical results demonstrate the convergence of the distributed solution procedure to the optimal solution, as well as the performance gains compared to other design methods. It is shown that the joint design scheme can accommodate double the traffic load, or achieve half the delay compared to the disjoint methods.