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) direction, and the probing field is time harmonic. The problem is solved with a rigorous integral method leading to a single boundary integral equation. This equation is converted into a linear system of equations, thanks to a boundary finite element method. To improve the accuracy, especially when the two boundaries are very close to each other, the singularity of the kernel is isolated and its integration is performed analytically. As shown through several examples, this versatile tool is well suited for the investigation of physical phenomena, especially the competition between surface and subsurface scattering.¿ 1997 American Geophysical Union