  Misfit compounds are thermodynamically stable stacks of two-dimensional
materials, forming a three-dimensional structure that remains incommensurate in
one direction parallel to the layers. As a consequence, no true bonding is
expected between the layers, with their interaction being dominated by charge
transfer. In contrast to this well-established picture, we show that interlayer
coupling can strongly influence the electronic properties of one type of layer
in a misfit structure, in a similar way to the creation of modified band
structures in an artificial moir\'e structure between two-dimensional
materials. Using angle-resolved photoemission spectroscopy with a micron-scale
light focus, we selectively probe the electronic properties of hexagonal
NbSe$_2$ and square BiSe layers that terminate the surface of the
(BiSe)$_{1+\delta}$NbSe$_2$ misfit compound. We show that the band structure in
the BiSe layers is strongly affected by the presence of the hexagonal NbSe$_2$
layers, leading to quasi one-dimensional electronic features. The electronic
structure of the NbSe$_2$ layers, on the other hand, is hardly influenced by
the presence of the BiSe. Using density functional theory calculations of the
unfolded band structures, we argue that the preferred modification of one type
of bands is mainly due to the atomic and orbital character of the states
involved, opening a promising way to design novel electronic states that
exploit the partially incommensurate character of the misfit compounds.
