  Fluid parts of the phase diagram of ${}^3$He -${}^4$He mixtures are obtained
from a mean-field analysis of a suitable lattice gas model for binary liquid
mixtures. The proposed model takes into account the continuous rotational
symmetry O(2) of the superfluid degrees of freedom associated with ${}^4$He and
includes the occurrence of vacancies. This latter degree of freedom allows the
model to exhibit a vapor phase and hence can provide the theoretical framework
to describe the experimental conditions for measurements of tricritical Casimir
forces in ${}^3$He -${}^4$He wetting films.
