We report on the development of a hybrid mirror realized by integrating an EUV-reflecting multilayer coating with a lamellar grating substrate. This hybrid mirror acts as an efficient Bragg reflector for extreme ultraviolet (EUV) radiation at a given wavelength while simultaneously providing spectral-selective suppression of the specular reflectance for unwanted longer-wavelength radiation due to the grating phase-shift resonance. The test structures, designed to suppress infrared (IR) radiation, were fabricated by masked deposition of a Si grating substrate followed by coating of the grating with a Mo/Si multilayer. To give the proof of principle, we developed such a hybrid mirror for the specific case of reflecting 13.5 nm radiation while suppressing 10 μm light, resulting in 61% reflectance at the wavelength of 13.5 nm together with the 70 × suppression rate of the specular reflection at the wavelength of 10 μm, but the considered filtering principle can be used for a variety of applications that are based on utilization of broadband radiation sources.