Despite the clear benefits of mechanical ventilation, it can also cause ventilator-induced lung injury, especially for critically ill patients suffering from Acute Lung Injury/ARDS. The main obstacles to more protective and individualized ventilation strategies are still insufficient knowledge and understanding of complex lung mechanics in healthy and diseased states, mainly due to the limited ability for in vivo measurement and imaging on the most relevant alveolar level. Even the most powerful computational approaches, however, only focus on investigating the effect of ventilation on air distribution, tissue strains/stresses, while coupling to the pulmonary circulation is mostly neglected. This is even though the lungs' main function, namely gas exchange, occurs through a dense network of pulmonary blood vessels in the alveolar walls. Hence, the coupling between respiratory system and pulmonary circulation is crucial for getting more insight into the main purpose of ventilation: adequate oxygen supply and carbon dioxide release while keeping the tissue in a healthy state. This contribution presents a physics-based, coupled, multi-dimensional, and multiphase poroelastic approach to computationally model airflow, blood flow, and gas exchange in human lungs. Motivated by the structure of the lungs, larger airways, and blood vessels are modeled as discrete 0D networks that are embedded into a 3D, three-phase (air, blood, and tissue) porous medium, representing the smaller airways, smaller blood vessels and lung tissue in a homogenized manner. Further, the respiratory gases, oxygen, and carbon dioxide are modeled as chemical subcomponents of air and blood with a suitable exchange model in the porous domain. To connect the homogenized and the discrete representations of airways and blood vessels, respectively, a 0D-3D coupling method is used, which allows a non-matching spatial discretization of both domains. The method couples fluid flow and species transport in these phases via an outflow condition from the tips of the discrete networks into the 3D porous medium and vice versa. Such a comprehensive approach allows us to study the complex interplay of tissue deformation and perfusion and its effects on oxygenation and carbon dioxide release. Further, the underlying multiphase model can easily be extended to include additional phases to study pathological conditions such as water accumulation in pulmonary edema in future model stages.