<p>Within the framework of the three-dimensional linearized stability theory for deformable solids, this study investigates the critical loading parameters corresponding to the loss of stability of a nonlinear-elastic (hyperelastic) strip located between two half-planes made of a different hyperelastic material, under compression along two parallel interphase cracks. Outside the defects, the components of the piecewise-homogeneous body are rigidly connected to each other. This problem geometry models a layered structure in which the intermediate layers are significantly thinner than the massive matrix, which is weakened by local defects. The corresponding critical deformations are determined from the solution of the eigenvalue problem for a system of Fredholm integral equations of the first kind. A parametric analysis conducted for the case where the composite materials are nonlinearly elastic and described by a harmonic elastic potential revealed a complex interaction of local and structural (macroscopic) mechanisms of instability that occur during compression. In particular, it has been established that when the ratio of the materials’ stiffnesses exceeds a certain threshold value, the behavior of the critical deformation becomes asymptotic: for short cracks, it strictly converges to values determined by the solution of a transcendental equation obtained for an identical piecewise-homogeneous body with perfectly joined layers.</p>