We report on observations of NGC 1068 with NuSTAR , which provide the best constraints to date on its > 10 keV spectral shape . The NuSTAR data are consistent with past instruments , with no strong continuum or line variability over the past two decades , consistent with its classification as a Compton-thick AGN . The combined NuSTAR , Chandra , XMM-Newton , and Swift BAT spectral dataset offers new insights into the complex secondary emission seen instead of the completely obscured transmitted nuclear continuum . The critical combination of the high signal-to-noise NuSTAR data and the decomposition of the nuclear and extranuclear emission 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 without requiring unrealistic physical parameters ( e.g. , large Fe overabundances , inconsistent viewing angles , poor fits to the spatially resolved spectra ) . A multi-component reflector with three distinct column densities ( e.g. , with best-fit values of N _ { H } = 1.5 \times 10 ^ { 23 } , 5 \times 10 ^ { 24 } , and 10 ^ { 25 } 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 } component provides the bulk of the flux to the Compton hump while the lower N _ { H } component produces much of the line emission , effectively decoupling two key features of Compton reflection . We also find that \approx 30 % of the neutral Fe K \alpha line flux arises from > 2″ ( \approx 140 pc ) and is clearly extended , 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 Compton-thick spectra from observations with poorer signal-to-noise and/or more distant objects .