We consider the 2D-problem of the reflection of a plane wave from non-identical layers of gratings made of fibers of arbitrary cross-section and presenting electric and magnetic contrasts with respect to the surrounding medium. The structure is of finite thickness and backed by a perfectly conducting plane. A domain integral equation is derived for the electric and magnetic currents in the fibers, from which the reflected field is computed. Comparisons with other approaches are made and examples are given to illustrate the absorbing properties of these structures.