This article presents the proposal, synthetic design, and implementation of a class of wideband bandpass frequency-selective structures (FSSs) with multiple in-band transmission poles. Each FSS element is formed by introducing parallel-coupled stepped-impedance slotline resonators (SISRs) on a printed circuit board (PCB). By periodically printing the FSS elements in long PCB pieces and then stacking them together with a certain distance, the incident spatial waves in free space can be converted into guided waves propagating along the slotline resonators of our proposed FSS and can be reconverted from guided waves into spatial waves. Therefore, the slotline resonators are designed to manipulate the incident spatial waves by controlling the filtering response of the guided waves within the FSS. An equivalent transmission-line (TL) model is then established to explain the manipulation mechanism. In order to systematically synthesize the filtering response, the transfer function of the equivalent TL model is mapped to the generalized Chebyshev equal-ripple response. The closed-form equations are derived, where all of the electrical and physical parameters are determined by the design specifications of in-band equal-ripple return loss (RL) and fractional bandwidth (FBW). To verify the theoretically predicted performances, three examples with different RLs (20, 30, and 10 dB) and FBWs (90%, 60%, and 120%) are designed, fabricated, and measured, respectively. The experimental results demonstrate that the proposed FSSs can achieve a desirable and stable wideband bandpass performance under oblique incidences. Our proposed method can also be applied to the design of other high-order wideband FSSs.