The support for multiple high-definition video streams in wireless home networks requires appropriate routing and rate control measures ascertaining the set of links for transmitting each stream and the encoding rate of the video to be delivered over the chosen links. The routing and rate allocation procedures impact the sustained quality of each video stream measured as the mean squared error distortion at the receiver, and the overall network congestion in terms of queuing delay per link. We study the trade-off between these two competing objectives in a united convex optimization formulation, and propose a distributed solutions for joint routing and rate control for multiple streams. For each stream, the optimal allocated rate strikes a balance between the selfish motive of minimizing video distortion and the global good of minimizing network congestions, while the routes are chosen over the least-congested links in the network. Simulation results are provided which demonstrate the effectiveness of our proposed joint routing and rate control scheme in the context of wireless home networks.