This paper proposes an extension of the recently proposed generalized spline nonlinear adaptive filter (GSNAF) to include suitable cross-terms which are products of input samples with different time shifts. In the proposed method, an adaptive spline function is extended to a two-dimensional adaptive function with two sets of inputs. The simulations show that in nonlinear system models having hard nonlinearities and cross-terms, the proposed filter can provide comparable or better performance compared to third-order Volterra filters and GSNAF.