  The normal state optical conductivity is calculated for a layered metal with
two layers per unit cell coupled through a transverse hopping matrix element
$t_\perp$. The optical response involves an interband term in addition to the
more familiar intraband term which leads to the usual Drude form. The interband
term is only weakly temperature dependent, even for an inelastic scattering
rate which is linear in T. It gives a $c$-axis response which extends in
frequency over the entire band width although there can be structure on this
energy scale which reflects details of the electronic structure. In particular,
at low energy, the $c$-axis response can develop a gap or pseudogap as the
temperature is lowered. At high temperature, a Drude response will be seen only
if the intraband transitions, which are of order $t_\perp^4$, become important
compared with the interband transitions which are of order $t_\perp^2$.
