  If the constituent particles of fluid phases interact via long-ranged van der
Waals forces, the effective Hamiltonian for \emph{interfaces} between such
fluid phases contains - in lateral Fourier space - non-analytic terms $ \sim
q^4 \ln q$. Similar non-analytic terms characterize the effective Hamiltonian
for two interacting interfaces which can emerge between the three possible
coexisting fluid phases in binary liquid mixtures. This is in contrast with the
structure of the phenomenological Helfrich Hamiltonian for membranes which does
not contain such non-analytic terms. We show that under favorable conditions
for the bulk densities characterizing a binary liquid mixture and for the
long-ranged interparticle interactions the corresponding effective Hamiltonian
for a model fluid \emph{membrane} does not exhibit such non-analytic
contributions. We discuss the properties of the resulting effective
Hamiltonian, with a particular emphasis on the influence of the long range of
the interactions on the coefficient of the bending rigidity.
