Recently, Özarslan and Elidemir (2023) proposed a novel methodology for constructing two-variable biorthogonal polynomial families by utilizing one-variable biorthogonal and orthogonal polynomial families. The primary objective of the paper is to introduce novel class of two-variable biorthogonal polynomials namely bivariate Jacobi Konhauser polynomials. We analyze various essential properties of these polynomials, such as their biorthogonality, operational formula, generating function, and integral representation. In addition, we examine the transformations of these polynomials under the Laplace transform, as well as their behavior under fractional integral and derivative operators. In the context of these polynomials, we introduce a new class of bivariate Jacobi-Konhauser-Mittag-Leffler (JKML) functions and derive corresponding properties for them. Furthermore, we define an integral operator whose kernel incorporates the bivariate JKML function and compute the images of power and exponential functions under its action. Finally, we explore the transformation of this operator under the Laplace transform.