  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].
