The airways and alveoli of the human respiratory tract are lined by two distinct types of epithelium, which are the primary targets of respiratory viruses. We previously established long-term expanding human lung epithelial organoids from lung tissues and developed a 'proximal' differentiation protocol to generate mucociliary airway organoids. However, a respiratory organoid system with bipotential of the airway and alveolar differentiation remains elusive. Here we defined a 'distal' differentiation approach to generate alveolar organoids from the same source for the derivation of airway organoids. The alveolar organoids consisting of type I and type II alveolar epithelial cells (AT1 and AT2, respectively) functionally simulate the alveolar epithelium. AT2 cells maintained in lung organoids serve as progenitor cells from which alveolar organoids derive. Moreover, alveolar organoids sustain a productive SARS-CoV-2 infection, albeit a lower replicative fitness was observed compared to that in airway organoids. We further optimized 2-dimensional (2D) airway organoids. Upon differentiation under a slightly acidic pH, the 2D airway organoids exhibit enhanced viral replication, representing an optimal in vitro correlate of respiratory epithelium for modeling the high infectivity of SARS-CoV-2. Notably, the higher infectivity and replicative fitness of the Omicron variant than an ancestral strain were accurately recapitulated in these optimized airway organoids. In conclusion, we have established a bipotential organoid culture system able to reproducibly expand the entire human respiratory epithelium in vitro for modeling respiratory diseases, including COVID-19.