We describe studies of new nanostructured materials consisting of carbon nanotubes wrapped in sequential coatings of two different semiconducting polymers, namely, poly(3-hexylthiophene) (P3HT) and poly(9,9'-dioctylfluorene-co-benzothiadiazole) (F8BT). Using absorption spectroscopy and steady-state and ultrafast photoluminescence measurements, we demonstrate the role of the different layer structures in controlling energy levels and charge transfer in both solution and film samples. By varying the simple solution processing steps, we can control the ordering and proportions of the wrapping polymers in the solid state. The resulting novel coaxial structures open up a variety of new applications for nanotube blends and are particularly promising for implementation into organic photovoltaic devices. The carbon nanotube template can also be used to optimize both the electronic properties and morphology of polymer composites in a much more controlled fashion than achieved previously, offering a route to producing a new generation of polymer nanostructures.