We report on observations of NGC1068 with NuSTAR, which provide the best constraints to date on its $>10$~keV spectral shape. We find no strong variability over the past two decades, consistent with its Compton-thick AGN classification. The combined NuSTAR, Chandra, XMM-Newton, and Swift-BAT spectral dataset offers new insights into the complex reflected emission. The critical combination of the high signal-to-noise NuSTAR data and a spatial decomposition with Chandra allow us to break several model degeneracies and greatly aid physical interpretation. When modeled as a monolithic (i.e., a single N_H) reflector, none of the common Compton-reflection models are able to match the neutral fluorescence lines and broad spectral shape of the Compton reflection. A multi-component reflector with three distinct column densities (e.g., N_H~1.5e23, 5e24, and 1e25 cm^{-2}) provides a more reasonable fit to the spectral lines and Compton hump, with near-solar Fe abundances. In this model, the higher N_H components provide the bulk of the Compton hump flux while the lower N_H component produces much of the line emission, effectively decoupling two key features of Compton reflection. We note that ~30% of the neutral Fe Kalpha line flux arises from >2 (~140 pc), implying that a significant fraction of the <10 keV reflected component arises from regions well outside of a parsec-scale torus. These results likely have ramifications for the interpretation of poorer signal-to-noise observations and/or more distant objects [Abridged].
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