  We study bivariate orthogonal polynomials associated with Freud weight
functions depending on real parameters. We analyze relations between the matrix
coefficients of the three term relations for the orthonormal polynomials as
well as the coefficients of the structure relations satisfied by these
bivariate semiclassical orthogonal polynomials, also a matrix
differential-difference equation for the bivariate orthogonal polynomials is
deduced. The extension of the Painlev\'e equation for the coefficients of the
three term relations to the bivariate case and a two dimensional version of the
Langmuir lattice are obtained.
