The transverse aperture-integral equation method provides a means of computation for diffraction coefficients at blunt edges of a broad class of stratified layers, including sheet-anisotropy models for conducting composites. In this paper we concentrate on the application of the method when the material profile comprises layers of homogeneous, potentially lossy material. The method proceeds from defining an artificial aperture perpendicular to a semi-infinite, planar, stratified region and passing through the terminal edge of the region. An integral equation is formulated over this infinite-extent aperture, and the solution to the integral equation represents the influence of the edge. The kernel in the integral equation is a weighted sum of the Green's functions for the respective half spaces lying on either side of the aperture plane. The vector wave equation is separable in each of these half spaces, resulting in Green's functions that are expressible analytically. The Green's function for the stratified half space is stated in terms of a Sommerfeld-type integral.