Influenza A virus (IAV) continuously causes epidemics and claims numerous lives every year. The available treatment options are insufficient and the limited pertinence of animal models for human IAV infections is hampering the development of new therapeutics. Bioprinted tissue models support studying pathogenic mechanisms and pathogen-host interactions in a human micro tissue environment. Here, we describe a human lung model, which consisted of a bioprinted base of primary human lung fibroblasts together with monocytic THP-1 cells, on top of which alveolar epithelial A549 cells were printed. Cells were embedded in a hydrogel consisting of alginate, gelatin and collagen. These constructs were kept in long-term culture for 35 days and their viability, expression of specific cell markers and general rheological parameters were analyzed. When the models were challenged with a combination of the bacterial toxins LPS and ATP, a release of the proinflammatory cytokines IL-1β and IL-8 was observed, confirming that the model can generate an immune response. In virus inhibition assays with the bioprinted lung model, the replication of a seasonal IAV strain was restricted by treatment with an antiviral agent in a dose-dependent manner. The printed lung construct provides an alveolar model to investigate pulmonary pathogenic biology and to support development of new therapeutics not only for IAV, but also for other viruses.