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Co-infections with respiratory viruses were reported in hospitalized patients in several cases. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and influenza A virus (IAV) are two respiratory viruses and are similar in terms of their seasonal occurrence, clinical manifestations, transmission routes, and related immune responses. SARS-CoV-2 is the cause of coronavirus disease 2019 (COVID-19). In this paper, we study the dynamic behaviors of an influenza and COVID-19 co-infection model in vivo. The role of humoral (antibody) immunity in controlling the co-infection is modeled. The model considers the interactions among uninfected epithelial cells (ECs), SARS-CoV-2-infected ECs, IAV-infected ECs, SARS-CoV-2 particles, IAV particles, SARS-CoV-2 antibodies, and IAV antibodies. The model is given by a system of delayed ordinary differential equations (DODEs), which include four time delays: (i) a delay in the SARS-CoV-2 infection of ECs, (ii) a delay in the IAV infection of ECs, (iii) a maturation delay of newly released SARS-CoV-2 virions, and (iv) a maturation delay of newly released IAV virions. We establish the non-negativity and boundedness of the solutions. We examine the existence and stability of all equilibria. The Lyapunov method is used to prove the global stability of all equilibria. The theoretical results are supported by performing numerical simulations. We discuss the effects of antiviral drugs and time delays on the dynamics of influenza and COVID-19 co-infection. It is noted that increasing the delay length has a similar influence to that of antiviral therapies in eradicating co-infection from the body. [ABSTRACT FROM AUTHOR]