Dependence of the initiation values of the Strain Energy Release Rate, GCi, on the orientation of the reinforcement direction α relative to the delamination front was investigated for two laminates of different interfacial ply arrangements. In the case of the first laminate, the delamination was located at the interface of the layers reinforced with symmetric fabric and unidirectional fabric. In the case of the second laminate, the delamination was located at the interface of layers reinforced with symmetric fabric. In both laminates, the orientation of fibers in the layers separated by the delamination differed by 45° regarding the warp directions. The investigations were carried out for Mode I, Mode II, and Mixed-Mode I/II (GII/GI = 1 and GII/GI = 1.7) loadings using hybrid beam specimens. The major problem appearing in the intended tests was the inevitable lack of symmetry in the xz and xy planes of the specimens and the resulting deformation and stress–strain couplings, causing undesired loading modes. To decrease these couplings, especially designed hybrid beam specimens were used. An auxiliary finite element analysis was performed to assess the remaining effects of the reduced couplings. To ascertain whether statistically significant differences between Gci values for different α occurred, the one-way analysis of variance supplemented by Levene’s test was carried out. The dependence of Gci on α was found out for both laminates. However, it was not equally strong, and it turned out that the loading mode and the interfacial ply were arrangement sensitive.