The direct scattering problem from a stack of two rough interfaces or
from a buried object with a rough interface above it is addressed. The
two boundaries are separating three homogeneous and isotropic media.
The profiles are assumed to be invariant in one (and the same) directi
on, and the probing field is time harmonic. The problem is solved with
a rigorous integral method leading to a single boundary integral equa
tion. This equation is converted into a linear system of equations, th
anks to a boundary finite element method. To improve the accuracy, esp
ecially when the two boundaries are very close to each other, the sing
ularity of the kernel is isolated and its integration is performed ana
lytically. As shown through several examples, this versatile tool is w
ell suited for the investigation of physical phenomena, especially the
competition between surface and subsurface scattering.