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-pharmacological 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 did not significantly interfere with A/H3N2 or 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. SARS-CoV-2 induced a marginal IFN production and reduced the IFN response during coinfections with influenza. 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.