We present analytical results for the contribution of electromagnetic fluctuations in
the distribution of interaction energy and pressure in isotropic systems whose
properties depend only on one spatial coordinate. If we neglect the continuous
inhomogeneity introduced here and consider the simplest case of two macroscopic
homogeneous bodies separated by a homogeneous film our result reduces to the
well-known Lifshitz formula. As a first application of theory, a one-dimensional
modulated system with a homogeneous layer embedded in it is considered and a
suitable perturbation theory for this system is developed. In the main part of
this paper we limit the calculations to the non-retarded case, that is only the
calculation of van der Waals interaction energy is given. As a second application
of theory we consider the van der Waals interaction between two semi-infinite
media across a planar region within which there is a thin film having an arbitrary
variation of the dielectric permittivity. The importance of the precise evaluation
of the transverse magnetic surface mode dispersion relation in inhomogeneous
media is elucidated. For concreteness the influence of the transition layer between
water and lipid in a symmetrical configuration is considered in some detail. The
zero-frequency term and the dispersion-only contribution to the Hamaker coefficient are
given analytically using some approximations and modelling of the dielectric
constants reasonable for these dielectrics at room temperature. As a whole the
results indicate the necessity of performing Lifshitz-type calculations on realistic
inhomogeneous layered models, as are the models described here, for accurate
interaction energy modelling. Of course further work is needed for real justification
of the continuous variation of dielectric permittivities across phase interfaces.