A new three-dimensional bandpass frequency-selective structure (FSS) is proposed for dual-polarized applications. Each square unit cell of the proposed FSS consists of vertical and horizontal double-sided parallel-strip lines (DSPSLs) and a thin metallic plate. Furthermore, the parallel-strip lines of every DSPSL are connected together through via holes. Using this arrangement, multimode resonators are established in the proposed structure. At lower frequencies, the substrate mode propagates and two resonators along the DSPSL are constructed, leading to a bandpass response with two transmission poles. At higher frequencies, the air mode is reflected by two resonates along the inserted plate, resulting in a stopband with two transmission zeros. The operating principle for this FSS is explained with the aid of an equivalent circuit model. Moreover, a parametric study of the proposed FSS is also carried out and design guidelines are formulated. As an example, a prototype of the proposed FSS is designed, fabricated, and tested. Measured results demonstrate that the FSS exhibits dual polarizations, high out-of-band rejection, and stable frequency response under both transverse electric (TE) and transverse magnetic (TM) polarizations of an obliquely incident wave.