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Techniques for forming sophisticated, 3D mesostructures in advanced, functional materials are of rapidly growing interest, owing to their potential uses across a broad range of fundamental and applied areas of application. Recently developed approaches to 3D assembly that rely on controlled buckling mechanics serve as versatile routes to 3D mesostructures in a diverse range of high-quality materials and length scales of relevance for 3D microsystems with unusual function and/or enhanced performance. Nonlinear buckling and delamination behaviors in materials that combine both weak and strong interfaces are foundational to the assembly process, but they can be difficult to control, especially for complex geometries. This paper presents theoretical and experimental studies of the fundamental aspects of adhesion and delamination in this context. By quantifying the effects of various essential parameters on these processes, we establish general design diagrams for different material systems, taking into account 4 dominant delamination states (wrinkling, partial delamination of the weak interface, full delamination of the weak interface, and partial delamination of the strong interface). These diagrams provide guidelines for the selection of engineering parameters that avoid interface-related failure, as demonstrated by a series of examples in 3D helical mesostructures and mesostructures that are reconfigurable based on the control of loading-path trajectories. Three-dimensional micromechanical resonators with frequencies that can be selected between 2 distinct values serve as demonstrative examples.