This study proposes a frequency-selective absorber (FSA) with dual passbands and wide-angle oblique incidence. The design consists of a circuit analog (CA) sheet and a dual-bandpass frequency selective surface (FSS) sheet, both embedded in dielectric slabs separated by a foam spacer. The CA sheet unit cell is based on a tripole loaded with multiple shorted transmission lines and lumped resistors. In this way, the performance of the CA sheet is equivalent to a resistive sheet in a low-frequency band and a transparent sheet in two high-frequency bands. By comprehensively designing the CA sheet and the dual-bandpass FSS sheet, we created an FSA structure that exhibits microwave absorption in the band from 2.6 GHz to 9.2 GHz with a reflectivity lower than -10 dB. It also possesses transmission in the 12.2-15.1 GHz and 30.6-31.5 GHz bands, with a transmittance greater than -3 dB in both. In addition, the FSA structure provides a stable transmission response of up to 60° of oblique incidence and absorption performance of up to 45° of oblique incidence in TE and TM polarization. A 400 × 400 mm flat FSA sample was fabricated, was measured, and is discussed. The experimental results are consistent with the simulation results, proving that the proposed FSA design holds great potential for applications in dual-frequency low-scattering radomes with high curvature and multi-directional electromagnetic interference suppression.