Various computational problems can be reduced to computing the marginals and the partition function of a suitably defined standard factor graph (S-FG). The sum-product algorithm (SPA) is an efficient iterative method for approximating these quantities, resulting in the so-called Bethe approximation of these quantities. In previous work, Vontobel proved that for an S-FG whose partition function equals the permanent of a nonnegative square matrix, the Bethe free energy function associated with the S-FG is a convex function and the SPA efficiently finds the minimum of the Bethe free energy function, from which the Bethe approximation of the permanent can be computed. We extend Vontobel's results by considering a class of bipartite S-FGs where each local function is defined based on a (possibly different) multi-affine homogeneous real stable polynomial. This class of S-FGs covers various combinatorial problems, including computing a generalization of the matrix permanent and determining the number of binary contingency tables with prescribed marginals. Results by Straszak and Vishnoi for a slightly larger class of S-FGs (they do not assume homogeneity of the polynomials) show that these S-FGs have the property that the Bethe partition function lower bounds the partition function. In this paper we prove, Various computational problems can be reduced to computing the marginals and the partition function of a suitably defined standard factor graph (S-FG). The sum-product algorithm (SPA) is an efficient iterative method for approximating these quantities, resulting in the so-called Bethe approximation of these quantities. In previous work, Vontobel proved that for an S-FG whose partition function equals the permanent of a nonnegative square matrix, the Bethe free energy function associated with the S-FG is a convex function and the SPA efficiently finds the minimum of the Bethe free energy function, from which the Bethe approximation of the permanent can be computed. We extend Vontobel's results by considering a class of bipartite S-FGs where each local function is defined based on a (possibly different) multi-affine homogeneous real stable polynomial. This class of S-FGs covers various combinatorial problems, including computing a generalization of the matrix permanent and determining the number of binary contingency tables with prescribed marginals. Results by Straszak and Vishnoi for a slightly larger class of S-FGs (they do not assume homogeneity of the polynomials) show that these S-FGs have the property that the Bethe partition function lower bounds the partition function. In this paper we prove, with the help of results for real stable polynomials and results from matroid theory, various statements for the class of S-FGs under consideration: we show that a certain projection of the local marginal polytope equals the convex hull of the set of valid configurations, that the Bethe free energy function possesses some convexity properties, and, for the typical case where the S-FG has an SPA fixed point consisting of positive-valued messages only, that the SPA finds the value of the Bethe partition function exponentially fast.with the help of results for real stable polynomials and results from matroid theory, various statements for the class of S-FGs under consideration: we show that a certain projection of the local marginal polytope equals the convex hull of the set of valid configurations, that the Bethe free energy function possesses some convexity properties, and, for the typical case where the S-FG has an SPA fixed point consisting of positive-valued messages only, that the SPA finds the value of the Bethe partition function exponentially fast.