This paper describes a relatively simple approach to calculating the frequency response for a two-dimensional (2-D) magnetic recording system with a medium that can include an arbitrary number of layers. Each layer may have an arbitrary magnetization direction, anisotropic permeability, and exchange coupling. The approach relies on an initial transformation into the spatial frequency domain and then the use of transmission matrices to relate the fields in the different layers. The approach is general in that it provides a method for finding the field configuration for any set of 2-D magnetic sources embedded in a layered magnetic medium with a linear B--H relationship. Here, we focus on calculating the readback response for a variety of longitudinal and perpendicular recording configurations. Since the permeability may have any wavelength dependence, we can easily include the effect of exchange coupling in the underlayer.