Motivated by the proliferation of dual radio devices, we consider a wireless network model in which all devices have short-range transmission capability, but a subset of the nodes has a secondary long-range wireless interface. For the resulting class of random graph models, we present analytical bounds for both the connectivity and the max-flow min-cut capacity. Perhaps the most striking conclusion to be drawn from our results is that the capacity of this class grows quadratically with the fraction of dual radio devices, thus indicating that a small percentage of such devices is sufficient to improve significantly the capacity of the network.