In this article, a class of bandpass frequency selective surfaces (FSSs) based on aperture-coupled dual-mode patch resonators (AC-DMPRs) are proposed to achieve single- and dualband high-order filtering responses with low profiles. Initially, a basic resonator of a square patch with diagonal corner truncations is theoretically investigated so as to demonstrate that two orthogonal modes can be simultaneously excited in a single patch resonator. Then, to eliminate the cross-polarized reflection caused by the orthogonal modes, a composite resonator, including four of such corner-truncated patches with 90 rotation between each two adjacent patches, is constructed and analyzed. Furthermore, by arranging two of such composite resonators in a back-to-back manner through coupling apertures on the middle metallic layer, an FSS element of three-layer AC-DMPR is formed. Compared with traditional aperture-coupled patch resonators (AC-PRs), the resonant modes of AC-DMPR are increased twice, thus giving more design flexibility to achieve high-order performance. To validate the design concept, a single-band fourth-order bandpass FSS is designed by introducing magnetic couplings in the ACDMPRs. Moreover, dual-band second-order bandpass FSSs with magnetic and/or electric couplings in the AC-DMPRs are also designed. Based on the even- and odd-mode analysis method, equivalent circuit models are established to explain the operating principles of the proposed structures. Finally, the designed FSSs are fabricated and measured. Good agreement between the measured and simulated results well validates the conceptual designs.