Covalent organic frameworks (COFs) are promising photocatalysts with excellent chemical stability, broad light absorption, and tailorable molecular structures. To assemble highly crystalline 2D (two-dimensional) COFs, planar molecular units like benzotrithiophene (BTT) and 2,2'-bipyridine (Bpy) are highly desired. Herein, two COFs are assembled by the condensation of benzo[1,2-b:3,4-b′:5,6-b′′]trithiophene-2,5,8-tricarbaldehyde with [2,2'-bipyridine]-5,5'-diacetonitrile and [2,2'-bipyridine]-5,5'-diamine, respectively. An sp2 carbon-linked COF Bpy-sp2c-BTT-COF and an imine-linked COF Bpy-IM-BTT-COF with apparent electron donor–acceptor configuration are readily furnished, in which the planarity of Bpy underpins their crystallinity. The sp2-carbon linkage plays a more crucial role than the imine linkage in adjusting band structure and facilitating electron transfer over Bpy-sp2c-BTT-COF and Bpy-IM-BTT-COF. Therefore, Bpy-sp2c-BTT-COF demonstrates superior performance than Bpy-IM-BTT-COF for selective sulfoxidation with oxygen driven by green light, in which superoxide and single oxygen are both involved during the activation of oxygen. The linkage selection for COFs opens new doors into visible light photocatalysts for selective conversions.