Microfluidic platforms are increasingly used to study blood microflows at true physiological scale. Indeed, lab-on-chip devices are overcoming the obstacle of manufacturing complex morphologies such as the organ-specific architectures of the microcirculation. In the present work, we utilize microfluidic platforms to devise in vitro models of the underlying pulmonary capillary networks (PCN), where capillary lengths and diameters are similar to the size of red blood cells (RBCs) ~ 5-10 µm. To better understand flow characteristics and dispersion of RBCs in PCNs, we have designed microfluidic models of alveolar capillary beds inspired by the seminal “sheet flow” model of Fung and Sobin (1969). Our biomimetic microfluidic PCNs feature confined arrays of staggered pillars with hydraulic diameters of 10 µm. The devices are perfused with suspensions of RBCs at varying hematocrit levels under different physiological flow rates. Whole-field velocity patterns using micro-PIV and single-cell tracking using PTV are obtained with fluorescently-labelled RBCs and discussed. Our experiments deliver a real-scale quantitative description of RBC perfusion characteristics across the pulmonary capillary microcirculation.