We report the growth of InAs/InAsSb single and double heterostructured nanowires by Au-assisted chemical beam epitaxy. The InAsSb nanowire segments have been characterized in a wide range of antimony compositions. Significant lateral growth is observed at intermediate compositions (x ~ 0.5), and the nucleation and step-flow mechanism leading to this lateral growth has been identified and described. Additionally, CuPt ordering of the alloy has been observed with high resolution transmission electron microscopy, and it is correlated to the lateral growth process. We also show that it is possible to regrow InAs above the InAsSb alloy segment, at least up to an intermediate antimony composition. Such double heterostructures might find applications both as mid-infrared detectors and as building blocks of electronic devices taking advantage of the outstanding electronic and thermal properties of antimonide compound semiconductors.