  A two-variable extension of the Bannai-Ito polynomials is presented. They are
obtained via $q\to-1$ limits of the bivariate $q$-Racah and Askey-Wilson
orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality
relation is obtained. These new polynomials are also shown to be multispectral.
Two Dunkl shift operators are seen to be diagonalized by the bivariate
Bannai-Ito polynomials and 3- and 9-term recurrence relations are provided.
