This article presents a design method for multilayer packaged single- and dual-band dual-channel bandpass filters (DCBPFs) based on square substrate integrated waveguide (SIW) cavities. By exploiting one or multiple pairs of orthogonal degenerate modes in square SIW resonators, two single-band and one dual-band DCBPFs with high channel isolations are implemented. By arranging feeding ports and coupling apertures, a highly selective single-band DCBPF with multiple types of operating states is demonstrated. In order to construct dual-band DCBPF design, balanced feeding ports are introduced to excite the operating modes and suppress unwanted spurious modes between the dual passbands, thus realizing a satisfactory dual-band frequency response. To validate the design method, two single-band and one dual-band prototypes are designed, fabricated, and measured. The results exhibit excellent filtering performance and high channel-to-channel isolations.