Due to the continuing high impact of lung diseases on society and the emergence of new respiratory viruses, such as SARS-CoV-2, there is a great need for in vitro lung models that more accurately recapitulate the in vivo situation than current models based on lung epithelial cell cultures on stiff membranes. Therefore, we developed an in vitro airway epithelial–endothelial cell culture model based on Calu-3 human lung epithelial cells and human lung microvascular endothelial cells (LMVECs), cultured on opposite sides of flexible porous poly(trimethylene carbonate) (PTMC) membranes. Calu-3 cells, cultured for two weeks at an air–liquid interface (ALI), showed good expression of the tight junction (TJ) protein Zonula Occludens 1 (ZO-1). LMVECs cultured submerged for three weeks were CD31-positive, but the expression was diffuse and not localized at the cell membrane. Barrier functions of the Calu-3 cell cultures and the co-cultures with LMVECs were good, as determined by electrical resistance measurements and fluorescein isothiocyanate-dextran (FITC-dextran) permeability assays. Importantly, the Calu-3/LMVEC co-cultures showed better cell viability and barrier function than mono-cultures. Moreover, there was no evidence for epithelial- and endothelial-to-mesenchymal transition (EMT and EndoMT, respectively) based on staining for the mesenchymal markers vimentin and α-SMA, respectively. These results indicate the potential of this new airway epithelial–endothelial model for lung research. In addition, since the PTMC membrane is flexible, the model can be expanded by introducing cyclic stretch for enabling mechanical stimulation of the cells. Furthermore, the model can form the basis for biomimetic airway epithelial–endothelial and alveolar–endothelial models with primary lung epithelial cells.