Cocontinuous nanostructured blends of semi-crystalline polymers tend to align along a preferential direction when subjected to steady flow. We investigate the flow induced changes experienced by cocontinuous blends using transmission electron microscopy and small-angle X-ray scattering and we demonstrate that shear flow induces a preferential direction while preserving a cocontinuous structure, which is oriented along the flow direction. In parallel, we study the viscoelastic properties of the aligned morphology by linear oscillatory shear above the melting temperature of the blend components and observe a liquid-like behavior at short times. Upon annealing at high temperature, the aligned morphology relaxes back to the original isotropic structure with a solid-like viscoelastic behavior.