A joint XMM-Newton and NuSTAR observation was conducted for the bright, local Seyfert 1.9 galaxy, NGC 1194. The hard spectral form of this AGN was modeled using the toroidal reprocessor MYTORUS. The decoupled model form provides a good description of the spectrum, with reflection arising from gas with a global average column density > 4 x 10^24 cm^-2 and transmission of the continuum through an order-of-magnitude lower column. In this model, the reflection strength is a factor ~3 higher than expected from a simple torus. Such a result may indicate that much of the intrinsic X-ray continuum is hidden from view. An alternative model is that of a patchy torus, where 85% of sight-lines are obscured by Compton-thick gas and the remaining 15% by Compton-thin gas. The patchy torus model is based on a solar abundance of Fe and is consistent with X-ray partial-covering results found in other AGN. That a patchy torus model would relieve the issue with the strength of the reflection signature is not an intuitive result: such an insight regarding the geometry of the global reprocessing gas could not have been obtained using ad hoc model components to describe the spectral form.