In this paper, we present certain tridiagonal matrices associated with generalized bivariate Fibonacci and Lucas polynomials and investigate the relationships between these matrices and polynomials. We show that determinants and permanents of these tridiagonal matrices are generalized bivariate Fibonacci and Lucas polynomials, which generalize known results for Fibonacci, Lucas, Pell, Jacobsthal, Fermat, Morgan-Voyce, and Vieta polynomials in both univariate and bivariate forms.