Lung related disorders like COPD and Asthma, as well as various infectious diseases, form a major therapeutic area which would benefit from a predictive and adaptable mathematical model for describing pulmonary disposition of biological modalities. In this study we fill that gap by extending the cross-species two-pore physiologically-based pharmacokinetic (PBPK) platform with more detailed respiratory tract that includes the airways and alveolar space with epithelial lining fluid. We parameterize the paracellular and FcRn-facilitated exchange pathways between the epithelial lining fluid and lung interstitial space by building a mechanistic model for the exchange between the two. The optimized two-pore PBPK model described pulmonary exposure of several systemically dosed mAbs for which data is available and is also in agreement with the observed levels of endogenous IgG and albumin. The proposed framework can be used to assess pharmacokinetics of new lung-targeting biologic therapies and guide their dosing to achieve desired exposure at the pulmonary site-of-action.