The role of a compliant adhesive interlayer in determining critical conditions for radial fracture at the undersurfaces of brittle coatings bonded to substrates of dissimilar materials is investigated. Semi-empirical relations for the critical loads are derived by treating the adhesive as part of an effective substrate, thereby reducing the problem to that of a bilayer. A finite-element analysis of a model silicon/epoxy/glass system is used to evaluate adjustable parameters in the analytical relations. In situ experimental observations of crack initiation on the same material system are used to verify these relations. The critical loads depend sensitively on the adhesive thickness and modulus. Delamination at the interface in poorly bonded specimens greatly reduces the critical loads. This analysis affords a basis for predicting the prospective fracture resistance of brittle coatings joined by adhesives.