The development of novel catalysts for degrading organic contaminants in water is a current hot topic in photocatalysis research for environmental protection. In this study, C3N5 nanosheet/Ag2CO3 nanocomposites (CNAC-X) were used as efficient photocatalysts for the visible-light-driven degradation of methylene blue (MB), and tetracycline hydrochloride (TC-HCl) was synthesized for the first time using a simple thermal oxidative exfoliation and in situ deposition method. Due to the synergistic effect of nanosheet structures, carbon defects, and Z-scheme heterojunctions, CNAC-10 exhibited the highest photocatalytic activity, with photodegradation efficiencies of 96.5% and 97.6% for MB (60 mg/L) and TC-HCl (50 mg/L) within 90 and 100 min, respectively. The radical trapping experiments showed that ·O2− and h+ played major roles in the photocatalytic effect of the CNAC-10 system. Furthermore, intermediates in the photodegradation of MB and TC-HCl were investigated to determine possible mineralization pathways. The results indicated that C3N5 nanosheet/Ag2CO3 photocatalysts prepared in this work could provide an effective reference for the treatment of organic wastewater.