With the concurrent circulations of SARS-CoV-2 omicron and influenza A viruses in the community, there is evidence showing co-infection with both viruses. However, disease severity may vary due to the complex immunity landscape of the patients and the neutralizing antibody waning status. The intrinsic dynamic relationship and pathological significance for such co-infections remain largely unknown. The replication kinetics and innate immune responses from the co-infections of SARS-CoV-2 (Omicron BA.1 and D614G variant) and influenza A viruses (pandemic H1N1, seasonal H3N2 and highly pathogenic avian H5N1) were characterized in human respiratory tissue explants, human airway, and alveolar epithelial cells. SARS-CoV-2 reduced the replication of influenza A viruses, but not vice versa, during co-infections in human bronchial tissues and airway epithelial cells. In lung tissues, the co-infections showed minimal effects on each other, but the viral replications of the two viruses were mutually reduced except for H1N1pdm in the alveolar epithelial cells irrespective of the enhancement of the ACE2 receptor. Notably, the co-infections showed a significant upregulation of the innate immune responses of SARS-CoV-2 in comparison to single infections in both respiratory epithelial cells, suggesting that co-infections of influenza A viruses potentially lead to more severe damage to the host than SARS-CoV-2 single infections.