Residual stresses in thin film structures significantly impact their mechanical properties and affect interface delamination. Highly compressively stressed thin films buckling is the predominant interfacial failure mode due to strain energy release. In the present study the effect of cross-sectional stress and microstructural gradients of thin films on the buckling behavior are explored in a model material system consisting of a thin Cu film sputtered onto glass and a highly compressively stressed 500 nm thick Mo overlayer causing buckling delamination at the Cu-glass interface. Employing synchrotron cross-sectional X-ray nano-diffraction, multiaxial X-ray elastic strain and microstructure distributions were explored across the cross-section of the adhering and buckled bilayer, respectively. In the adhering state, a gradual thickness evolution of columnar microstructure and residual stress was found for Mo, while in Cu, no microstructure changes and only minimal stress variations were detected along the film thickness. After delamination, diffraction peak broadening and changes in unstrained lattice parameters in the Cu sublayer indicated structural defect annihilation and grain coarsening. These microstructural changes were further validated via cross-sectional transmission electron microscopy. The evaluated residual stress distributions across the two sublayers of the pristine and buckled bilayer were used to quantify the released strain energy per unit area due to buckling, amounting to 0.61 J/m². Further cross-validation of experimental stress results with finite element simulations strengthened the experimental findings, providing a comprehensive understanding of the stress distribution across the buckled bilayer.