The atomic structure at the interface between a two-dimensional (2D) and a three-dimensional (3D) material influences properties such as contact resistance, photo-response, and high-frequency performance. Moiré engineering has yet to be explored for tailoring this 2D/3D interface, despite its success in enabling correlated physics at 2D/2D twisted van der Waals interfaces. Using epitaxially aligned MoS₂ /Au{111} as a model system, we apply a geometric convolution technique and four-dimensional scanning transmission electron microscopy (4D STEM) to show that the 3D nature of the Au structure generates two coexisting moiré periods (18 Angstroms and 32 Angstroms) at the 2D/3D interface that are otherwise hidden in conventional electron microscopy imaging. We show, via ab initio electronic structure calculations, that charge density is modulated with the longer of these moiré periods, illustrating the potential for (opto-)electronic modulation via moiré engineering at the 2D/3D interface.