We study certain polynomials Pm (x, y;t) and Qm (x, y;t) of the variable t whose
coefficients involve bivariate Fibonacci polynomials Fj (x, y) or bivariate Lucas polynomials Lj (x, y). By working with Pm (x, y;tx) and Qm (x, y;tx), together with the
generating functions for Bernoulli polynomials Bi (t) and Euler polynomials Ei (t), we
obtain a list of eight identities connecting Fj (x, y) or Lj (x, y) with Bi (t) or Ei (t). We
present also some consequences of these results.