A thin broadband dual-layer radar absorber based on periodic Frequency Selective Surfaces (FSS) to tackle Electromagnetic Interference (EMI) in radomes is presented in this article. The proposed structure consists of periodically arranged metallic patterns printed on two dielectric substrates separated by an optimized air gap. Under normal incidence, the proposed structure exhibits at least 89.7% of absorption in the whole band of 4.8 GHz to 11.1 GHz for both Transverse Electric (TE) and Magnetic (TM) polarizations. For oblique incidences, a very slight decrease in the bandwidth is observed in the upper frequency band until 30° and the absorption remains very interesting for higher incidences. The structure is λ/7.2 (λ is the wavelength in free space) thin compared to the center frequency (8.2 GHz). In addition, parametric studies have demonstrated that at least 90% of absorption can be produced with our structure by adjusting the thicknesses of the dielectric substrates. Another issue that is presented and discussed in this paper is a new approach for evaluating the performance of absorbers. In fact, studies show that the absorber can compete with other recent broadband absorbers. After fabricating the structure, the measurements were found to be in good agreement with the simulation results.