Many emerging technologies such as wearable batteries and electronics require stretchable functional structures made from intrinsically less deformable materials. The stretch capability of most demonstrated stretchable structures often relies on either initially out‐of‐plane configurations or the out‐of‐plane deflection of planar patterns. Such nonplanar features may dramatically increase the surface roughness, cause poor adhesion and adverse effects on subsequent multilayer processing, thereby posing a great challenge for flexible devices that require smooth surfaces (e.g., transparent electrodes in which flat‐surface‐enabled high optical transmittance is preferred). Inspired by the lamellar layouts of collagenous tissues, this work demonstrates a planar bilayer lattice structure, which can elongate substantially via only in‐plane motion and thus maintain a smooth surfaces. The constructed bilayer lattice exhibits a large stretchability up to 360%, far beyond the inherent deformability of the brittle constituent material and comparable to that of state‐of‐the‐art stretchable structures for flexible electronics. A stretchable conductor employing the bilayer lattice designs can remain electrically conductive at a strain of 300%, demonstrating the functionality and potential applications of the bilayer lattice structure. This design opens a new avenue for the development of stretchable structures that demand smooth surfaces.