  The Casimir interaction between two thin material films, between a film and a
thick plate and between two films deposited on substrates is considered at
large separations (high temperatures) which correspond to the classical limit.
It is shown that the free energy of the classical Casimir interaction between
two insulating films with no free charge carriers and between an insulating
film and a material plate depends on film thicknesses and decreases with
separation more rapidly than the classical limit for two thick plates. The free
energy of thin films characterized by the metallic-type dielectric permittivity
decreases as the second power of separation, i.e., demonstrates the standard
classical limit. The obtained results shed light on the possibility to describe
dispersion interaction between two graphene sheets and between a graphene sheet
and a material plate by modeling graphene as a thin film possessing some
dielectric permittivity. It is argued that the most reliable results are
obtained by describing the reflection properties on graphene by means of the
polarization tensor in (2+1)-dimensional space-time.
