Precise vertical stacking and lateral stitching of two-dimensional (2D) materials, such as graphene and hexagonal boron nitride (h-BN), can be used to create ultrathin heterostructures with complex functionalities, but this diversity of behaviors also makes these new materials difficult to characterize. We report a DUV-vis-NIR hyperspectral microscope that provides imaging and spectroscopy at energies of up to 6.2 eV, allowing comprehensive, all-optical mapping of chemical composition in graphene/h-BN lateral heterojunctions and interlayer rotations in twisted bilayer graphene (tBLG). With the addition of transmission electron microscopy, we obtain quantitative structure-property relationships, confirming the formation of interfaces in graphene/h-BN lateral heterojunctions that are abrupt on a micrometer scale, and a one-to-one relationship between twist angle and interlayer optical resonances in tBLG. Furthermore, we perform similar hyperspectral imaging of samples that are supported on a nontransparent silicon/SiO2 substrate, enabling facile fabrication of atomically thin heterostructure devices with known composition and structure.