With the outbreak of new respiratory viruses and high mortality rates of pulmonary diseases, physiologically relevant models of human respiratory system are urgently needed to study disease pathogenesis, drug efficacy, and pharmaceutics. In this paper, a 3D alveolar barrier model fabricated by printing four human alveolar cell lines, namely, type I and II alveolar cells (NCI-H1703 and NCI-H441), lung fibroblasts (MRC5), and lung microvascular endothelial cells (HULEC-5a) is presented. Automated high-resolution deposition of alveolar cells by drop-on-demand inkjet printing enables to fabricate a three-layered alveolar barrier model with an unprecedented thickness of ≈10 µm. The results show that the 3D structured model better recapitulate the structure, morphologies, and functions of the lung tissue, compared not only to a conventional 2D cell culture model, as expected, but also a 3D non-structured model of a homogeneous mixture of the alveolar cells and collagen. Finally, it is demonstrated that this thin multilayered model reproduce practical tissue-level responses to influenza infection. Drop-on-demand inkjet-printing is an enabling technology for customization, scalable manufacturing, and standardization of their size and growth, and it is believed that this 3D alveolar barrier model can be used as an alternative to traditional test models for pathological and pharmaceutical applications.