Abstract Some respiratory viruses can cause a viral interference through the activation of the interferon (IFN) pathway that reduces the replication of another virus. Epidemiological studies of coinfections between SARS-CoV-2 and other respiratory viruses have been hampered by non-pharmaceutical measures applied to mitigate the spread of SARS-CoV-2 during the COVID-19 pandemic. With the ease of these interventions, SARS-CoV-2 and influenza A viruses can now co-circulate. It is thus of prime importance to characterize their interactions. In this work, we investigated viral interference effects between an Omicron variant and a contemporary influenza A/H3N2 strain, in comparison with an ancestral SARS-CoV-2 strain and the 2009 pandemic influenza A/H1N1 virus. We infected nasal human airway epitheliums with SARS-CoV-2 and influenza, either simultaneously or 24 h apart. Viral load was measured by RT-qPCR and IFN-α/β/λ1/λ2 proteins were quantified by immunoassay. Expression of four interferon-stimulated genes (ISGs; OAS1/IFITM3/ISG15/MxA) was also measured by RT-droplet digital PCR. Additionally, susceptibility of each virus to IFN-α/β/λ2 recombinant proteins was determined. Our results showed that influenza A, and especially A/H3N2, interfered with both SARS-CoV-2 viruses, but that SARS-CoV-2 only interfered with A/H1N1. Consistently with these results, influenza, and particularly the A/H3N2 strain, caused a higher production of IFN proteins and expression of ISGs than SARS-CoV-2. The IFN production induced by SARS-CoV-2 was marginal and its presence during coinfections with influenza was associated with a reduced IFN response. All viruses were susceptible to exogenous IFNs, with the ancestral SARS-CoV-2 and Omicron being less susceptible to type I and type III IFNs, respectively. Thus, influenza A causes a viral interference towards SARS-CoV-2 most likely through an IFN response. The opposite is not necessarily true, and a concurrent infection with both viruses leads to a lower IFN response. Taken together, these results help us to understand how SARS-CoV-2 interacts with another major respiratory pathogen. Author summary During the COVID-19 pandemic, non-pharmaceutical measures were able to reduce the spread of SARS-CoV-2 and most respiratory viruses. Since the ease of these measures, SARS-CoV-2 variants and other viruses, such as influenza A, have started to co-circulate and can now infect a same host and interact with each other. These interactions can lead to attenuated or aggravated infections and can affect the timing of epidemics. Therefore, it is very important to elucidate how the new SARS-CoV-2 interacts with other viruses to better predict their implications in human health and their epidemic activity. Our work contributes to better understand these interactions using viruses that have likely co-circulated after lifting mitigation interventions, i.e., SARS-CoV-2 Omicron variant and a contemporary influenza A/H3N2 strain. We studied how each virus may affect the other virus’ growth and how these interactions were associated with the innate immune response of the host. We found that a prior infection with influenza A can decrease the growth of SARS-CoV-2 while the latter reduces the innate immune response. Our results help to understand the interplay between SARS-CoV-2 and influenza A in the host and may improve mathematical models predicting epidemics.