We have developed a multilayer mirror for extreme UV (EUV) radiation (13.5 nm), which has near-zero reflectance for IR line radiation (10.6 μm). The EUV reflecting multilayer is based on alternating B4C and Si layers. Substantial transparency of these materials with respect to the IR radiation allowed the integration of the multilayer coating in a resonant quarter-wave structure for 10.6 μm. Samples were manufactured using magnetron sputtering deposition technique and demonstrated suppression of the IR radiation by up to 3 orders of magnitude. The EUV peak reflectance amounts 45% at 13.5 nm, with a bandwidth at FWHM being 0.284 nm. Therefore such a mirror could replace conventional multilayer mirrors to suppress undesired spectral components in monochromatic imaging applications, including EUV photolithography.