  Antiferromagnetic FeSn is considered to be a close realization of the ideal
two-dimensional (2D) kagome lattice, hosting Dirac cones, van Hove
singularities, and flat bands, as it comprises Fe$_3$Sn kagome layers well
separated by Sn buffer layers. We observe a pronounced optical anisotropy, with
the low-energy optical conductivity being surprisingly higher perpendicular to
the kagome planes than along the layers. This finding contradicts the prevalent
picture of dominantly 2D electronic structure for FeSn. Our material-specific
theory reproduces the measured conductivity spectra remarkarbly well. A
site-specific decomposition of the optical response to individual excitation
channels shows that the optical conductivity for polarizations both parallel
and perpendicular to the kagome plane is dominated by interlayer transitions
between kagome layers and adjacent Sn-based layers. Moreover, the matrix
elements corresponding to these transitions are highly anisotropic, leading to
larger out-of-plane conductivity. Our results evidence the crucial role of
interstitial layers in charge dynamics even in seemingly 2D systems.
