Biological interfaces often achieve high strength and damage tolerance through geometrically complex, interlocking patterns. Motivated by these natural designs, we develop an explicit interface geometry optimization framework in which the interface geometry is the primary design variable and nonlinear interfacial separation is modeled by cohesive laws. Complex interface geometries are represented explicitly by shear-stitching multiple parameterized curves, enabling precise geometric control independent of the analysis mesh. The multiphase response with displacement discontinuities is solved efficiently on a fixed mesh using the extended finite element method, together with an incremental-iterative scheme and viscous regularization for robust convergence. For interface strengthening, we formulate an objective that suppresses the maximum effective opening displacement of the interface and derive fully analytical shape sensitivities within a variational and adjoint framework, accounting explicitly for both geometric and state dependence. Numerical studies show that the optimization spontaneously generates complex interlocking features of varying forms, leading to substantial reductions in peak opening displacement under diverse loading and interface complexity. Experiments further confirm marked improvements in load capacity and energy dissipation for optimized interfaces compared with classical bio-inspired geometries. The resulting designs exhibit strong similarity to biological sutures, offering mechanistic insight into how complex interfacial morphologies may emerge through mechanical adaptation.