  We perform first-principles band structure calculations for the tetragonal
and monoclinic structures of LaO$_{0.5}$F$_{0.5}$BiS$_2$. We find that the Bi
$6p_{x,y}$ bands on two BiS$_2$ layers exhibit a sizable splitting at the X =
($\pi$, 0, 0) and several other \textbf{k}-points for the monoclinic structure.
We show that this feature originates from the inter-BiS$_2$ layer coupling
strongly enhanced by the symmetry breaking of the crystal structure. The Fermi
surface also shows a large splitting and becomes anisotropic with respect to
the $k_x$ and $k_y$ directions in the monoclinic structure, whereas it remains
almost flat with respect to the $k_z$ direction.
