The decohesion of coatings, thin films, or layers used to protect or strengthen technological and structural components causes the loss of their functions. In this paper, analytical, computational, and semi-analytical 2D solutions are derived for the energy release rate and mode-mixity phase angle of an edge-delamination crack between a thin layer and an infinitely deep substrate. The thin layer is subjected to general edge loading: axial and shear forces and bending moment. The solutions are presented in terms of elementary crack tip loads and apply to a wide range of material combinations, with a large mismatch of the elastic constants (isotropic materials with Dundurs’ parameters $-1\le \alpha \le 1$ and $-0.4\le \beta \le 0.4$ ). Results show that for stiff layers over soft substrates ( $\alpha \to 1$ ), the effects of material compressibility are weak, and the assumption of substrate incompressibility is accurate; for other combinations, including soft layers over stiff substrates ( $\alpha \to -1$ ), the effects may be relevant and problem specific. The solutions are applicable to edge- and buckling-delamination of thin layers bonded to thick substrates, to mixed-mode fracture characterization test methods, and as benchmark cases.