When a thin stiff film adhered to a compliant substrate is subject to compressive stresses, the film will experience a geometric instability and buckle out of plane. For high film/substrate stiffness ratios with relatively low levels of strain, the primary mode of instability will either be wrinkling or buckling delamination depending on the material and geometric properties of the system. Previous works approach these systems by treating the film and substrate as homogenous layers, either consistently perfectly attached, or perfectly unattached at interfacial flaws. However, this approach neglects systems where the film and substrate are uniformly weakly attached or where interfacial layers due to surface modifications in either the film or substrate are present. Here we demonstrate a method for accounting for these additional thin surface layers via an analytical solution verified by numerical results. The main outcome of this work is an improved understanding of how these layers influence global behavior. We demonstrate the utility of our model with applications ranging from buckling based metrology in ultrathin films, to an improved understanding of the formation of a novel surface in carbon nanotube bio-interface films. Moving forward, this model can be used to interpret experimental results, particularly for systems which deviate from traditional behavior, and aid in the evaluation and design of future film/substrate systems.