A layered architecture endows structural materials like nacre and biomimetic ceramics with enhanced mechanical performance because it introduces multiple strengthening and toughening mechanisms. Yet present studies predominantly involve enhancing the alignment in planar lamellar structures, and the effects of the stacking curvature have largely remained unexplored. Here we find that ordered curved stacking bands in lamellar structures act as a new structural mechanism to simultaneously improve strength and toughness. Aligned curved bands increase interlayer frictional resistance to show a strengthening effect and suppress the crack propagation to show an extrinsic toughening effect. In prototypical graphene oxide films, rational regulation of the intervals and orientations of curved bands bring a maximum 162% improvement in strength and 183% improvement in toughness simultaneously. Our results reveal the hidden effects of the stacking curvature on the mechanical behaviors of lamellar materials, opening an extra design dimension to fabricate stronger and tougher structural materials.