High-order bandpass filtering responses are highly desirable for frequency-selective surfaces (FSSs) in narrowband antenna/radar systems. In this paper, the design process of a reconfigurable dual-band FSS with second-order response is presented. Initially, the basic dumbbell-shaped resonator used in this design is theoretically investigated using the characteristic mode analysis (CMA) method to study the relation between geometric design parameters and the excited orthogonal resonance modes in different frequency bands. Then, an additional CMA process was performed on a unit cell with four such patch resonators arranged with 90-degree rotation between adjacent ones. This detailed analysis leads to a polarization-independent FSS design with a high-order dual-band response. Two of these composite resonators are combined back-to-back through coupling apertures on the middle layer. Finally, PIN diodes are loaded on separate layers to realize independent pass-band switching. The loading place of the PIN diodes is carefully chosen based on electromagnetic field analysis. A prototype was also fabricated and experimentally tested. Experimental results show that this FSS has two independently switchable passbands centered at 3 GHz and 4.8 GHz.