Joints and interfaces are one of the key aspects of the design and production of composite structures. This paper investigates the effect of adhesive–adherend interface morphology on the mechanical behavior of wavy-lap joints with the aim to improve the mechanical performance. Intentional deviation from a flat joint plane was introduced in different bond angles (0°, 60°, 90° and 120°) and the joints were subjected to a quasi-static tensile load. Comparisons were made regarding the mechanical behavior of the conventional flat joint and the wavy joints. The visible failure modes that occurred within each of the joint configurations was also highlighted and explained. Load vs. displacement graphs were produced and compared, as well as the failure modes discussed both visually and qualitatively. It was observed that distinct interface morphologies result in variation in the load–displacement curve and damage types. The wavy-lap joints experience a considerably higher displacement due to the additional bending in the joint area, and the initial damage starts occurring at a higher displacement. However, the load level had its maximum value for the single-lap joints. Our findings provide insight for the development of different interface morphology angle variation to optimize the joints behavior, which is widely observed in some biological systems to improve their performance.