Dual-band cold mirrors are designed based on third-order of 121.6 nm multilayers, and they are only composed of LaF3 and MgF2. The designed mirrors have a high reflectance at 121.6 nm and 280 nm, and a low reflectance in visible waveband; they also have a narrow bandwidth of 4 nm at 121.6 nm, and low sidelobe ripples of two stopbands. A broadband antireflection coating and an asymmetrically Gaussian-apodization of thickness-modulated design method are proposed to eliminate sidelobe ripples of the reflection zone.