The full wave solutions for the vertically and horizontally polarized electromagnetic fields scattered by irregular stratified media are expressed in terms of double infinite sums. These full wave solutions satisfy the reciprocity relationships in electromagnetic theory. The physical interpretation of each term in the double infinite series provides insights into the nonspecular scattering phenomena for irregular stratified media. It is shown that n+1 different terms of the full wave expansion replace the single nth term of the corresponding geometric optics series. From scattering in the specular direction these n+1 terms become analytically indistinguishable, and the full wave solution reduces to the geometric optics solution. The full wave solutions are also consistent with Rice's perturbation solution for rough surface scattering in the low-frequency limit. The physical interpretation of the full wave solutions which are based on complete spectral expansions of the fields could be used to construct solutions for the nonspecularly scattered fields in complex problems involving irregular stratified media.