The problem of identifying a discrete-time nonlinear system composed by interconnected linear and nonlinear subsystems is addressed in this paper. A representation based on linear fractional transformations is adopted to model the considered class of systems. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure.