We have developed a technique so that both transmission electron microscopy and microphotoluminescence can be performed on the same semiconductor nanowire over a large range of optical power, thus allowing us to directly correlate structural and optical properties of rotationally twinned zinc blende InP nanowires. We have constructed the energy band diagram of the resulting multiquantum well heterostructure and have performed detailed quantum mechanical calculations of the electron and hole wave functions. The excitation power dependent blue-shift of the photoluminescence can be explained in terms of the predicted staggered band alignment of the rotationally twinned zinc blende/wurzite InP heterostructure and of the concomitant diagonal transitions between localized electron and hole states responsible for radiative recombination. The ability of rotational twinning to introduce a heterostructure in a chemically homogeneous nanowire material and alter in a major way its optical properties opens new possibilities for band-structure engineering.