Mechanical ventilation is a life-saving therapy for patients with impaired pulmonary function, but it carries the risk of ventilator-induced lung injury (VILI). The development of protective ventilation strategies is limited by the insufficient understanding of complex lung mechanics, largely due to the limited ability for in vivo measurements. Computational modeling offers a promising path to shed light into this issue non-invasively, yet representing the lung’s multiscale structure and multiple interacting physical fields remains challenging. Most existing lung models primarily focus on ventilation-induced tissue deformation, while coupling to the pulmonary circulation is largely neglected, despite gas exchange taking place within the alveolar-capillary network. Hence, coupling between the respiratory system and pulmonary circulation is crucial for gaining a deeper understanding of the main purpose of ventilation: adequate gas exchange while maintaining tissue health. In this contribution, we present a physics-based, coupled mixed-dimensional and multiphase porous media framework for modeling airflow, blood flow, and gas exchange in the human lungs. Larger airways and blood vessels are represented as spatially resolved discrete networks of zero-dimensional elements, which are embedded into a deforming three-dimensional porous medium representing the smaller respiratory and vascular structures in a homogenized manner. Oxygen and carbon dioxide are modeled as chemical subcomponents of air and blood, with exchange occurring within 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. Such a comprehensive approach allows to study the complex interplay of ventilation, tissue deformation, perfusion, and its effects on gas exchange. Further, the model can be extended to study pathological conditions such as pulmonary edema by incorporating an additional phase. This approach allows to address some highly relevant clinical questions in respiratory care for the first time.