Transport computations in shield-tissue composite systems are presented. It is observed that the scattered gamma-ray spectra at the interface, which are governed by the reflectivities of different media, are significantly different from those of an infinite medium. The interface effects also extend back into the shield medium, the extent depending on the atomic number of the medium and energy of the source photons. The implications of these differences on the dose distribution and buildup factors in the shield-tissue system are significant. These studies show that in many cases the infinite-medium buildup factors are quite inadequate to compute the maximum dose in the tissue following a shield. Appropriate correction factors are given. The singular behavior of the spectrum due to source photons of energy close to but above the K edge of the medium is highlighted.