  We derive analytic expressions for the classical Casimir-Polder free energy
and force for a polarizable (magnetizable) atom (microparticle) interacting
with thin films, made of different materials, or graphene. It is shown that for
an isolated dielectric film the free energy and force decrease quicker with
separation, as compared to the case of atom interacting with a thick plate
(semispace). For metallic films some peculiar features depending on the model
of a metal used are analyzed. For an atom interacting with graphene we
demonstrate that at room temperature the classical regime is achieved at about
$1.5\,\mu$m separation. In this regime the contributions to the free energy and
force due to atomic magnetic polarizability are suppressed, as compared to main
terms caused by the atomic electric polarizability. According to our results,
at separations above $5\,\mu$m the Casimir-Polder interaction of atoms with
graphene is of the same strength as with an ideal-metal plane. The classical
interaction of atoms with thin films deposited on substrates is also
considered.
