Fabry-Perot (FP)-like resonances have been widely described in nanoantennas. In the original FP resonator, a third mirror can be added, resulting in a multimirror interferometer. However, in the case of a combination of nanoantennas, it has been reported that each cavity behaves independently. Here, we evidence the interferences between two FP absorbing nanoantennas through a common mirror, which has a strong impact on the optical behavior. While the resonance wavelength is only slightly shifted, the level of absorption reaches nearly 100%. Moreover, the quality factor increases up to factor 7 and can be chosen by geometric design over a range from 11 to 75. We demonstrate, thanks to a simple analytical model, that this coupling can be ascribed to a double FP cavity resonance, with the unique feature that each cavity is separately coupled to the outer medium.