We have developed a multilayer mirror for extreme ultraviolet (EUV) radiation that has low reflectance for IR radiation at 10.6 mum wavelength. The mirror is based on a multilayer coating comprising alternating layers of diamondlike carbon and silicon, for which we demonstrate an EUV reflectance of up to 49.7%. We have made a functional prototype in which the multilayer coating is included as part of an antireflection coating for IR radiation, resulting in reflectance values of 42.5% and 4.4% for EUV and IR, respectively. The mirror can replace a standard Mo/Si mirror in an EUV lithography tool to form an efficient solution for the suppression of unwanted CO(2) laser radiation.