We present joint radio selection and relay scheme that delivers data from a source to a sink in heterogeneous stationary sensor networks consisting of various radio interfaces. The proposed scheme finds the optimal relay nodes and their corresponding radio interfaces that minimize energy consumption throughout the network while satisfying the end-to-end packet deadline requirement. We formulate the problem of routing through radio interface selection into binary integer programs, and obtain the optimal solution by solving with an optimization solver. We examine a trade-off relationship between energy consumption and packet delay based on network level simulations. We show that given the end-to-end deadline requirement, our routing algorithm finds the most energy-efficient routing path and radio interface across mesh hops. We demonstrate that the proposed routing scheme exploits the given packet delivery time to turn into network benefit of reducing energy consumption compared to routing based on single radio interface.