A new procedure to identify the parameters of an unknown two-dimensional shift-invariant ARMA system has been presented. This procedure uses the formerly proposed two-channel AR lattice modeling approach and extends it to the case where the AR and MA parts of the ARMA process can take arbitrary values different from each other. The new proposed procedure can be named as a "hybrid lattice structure" where both two-channel and single channel lattice stages are involved. We also propose a new formulation to compute the ARMA parameters taking into account the parameter b(0) and the forward prediction error filter tap weights of both channels. Computer simulations have been carried out to verify the proposed method. This method can be applied to both quarter-plane and asymmetric half plane models.