In this paper, we investigate the information-theoretic performance of the multi-band relay channel which is defined by a source node, a relay node, and a destination node communicating over multiple orthogonal bands. The model is motivated by the vision of hybrid wireless networks where links operating with different communication standards relay information from the source to the destination. We consider hybrid wireless networks, with cognitive and agile radios, where bandwidth and power are the shared resources between different systems. We first provide the capacity bounds and find the optimum resource allocation that maximizes the achievable rate for a simple network. Based on the allocation strategy found, we next study the impact of optimum resource allocation on the construction of a hybrid wireless network, in particular, the scenario where a new source to relay and destination band is added to a classical frequency division relay network. Given the channel conditions of the network, we establish the guidelines on how to allocate resources in order to achieve the higher achievable rates, depending on the relative quality of the available links.