Studying nanostructured hierarchical materials such as the biomineralized bone is challenging due to their complex 3D structures that call for high spatial resolution. One route to study such materials is X-ray powder diffraction computed tomography (XRD-CT) that reveals the 3D distribution of crystalline phases and X-ray fluorescence computed tomography (XRF-CT) that provides element distributions. However, the spatial resolution of XRD-CT has thus far been limited. Here we demonstrate better than 120 nm 3D resolution on human bone in XRD-CT and XRF-CT measured simultaneously using X-ray nanobeams. The results pave the way for nanoscale 3D characterization of nanocrystalline composites like bone at unprecedented detail.