UNLABELLED: The health and function of microvascular beds are dramatically impacted by the mechanical forces that they experience due to fluid flow. These fluid flow-generated forces are challenging to measure directly and are typically calculated from experimental flow data. However, current computational fluid dynamics (CFD) models either employ truncated 2D models or overlook the presence of extraluminal flows within the interstitial space between vessels that result from the permeability of the endothelium lining the vessels, which are crucial components affecting flow dynamics. To address this, we present a bottom-up modeling approach that assesses fluid flow in 3D-engineered vessel networks featuring an endothelial lining and interstitial space. Using image processing algorithms to segment 3D confocal image stacks from engineered capillary networks, we reconstructed a 3D computational model of the networks. We incorporated vascular permeability and matrix porosity values to model the contributions of the endothelial lining and interstitial spaces to the flow dynamics in the networks. Simulations suggest that including the endothelial monolayer and the interstitium significantly affects the predicted flow magnitude in the vessels and flow profiles in the interstitium. To demonstrate the importance of these factors, we showed experimentally and computationally that while cytokine (IL-1β) treatment did not affect the network architecture, it significantly increased vessel permeability and resulted in a dramatic decrease in wall shear stresses and flow velocities intraluminally within the networks. In conclusion, this framework offers a robust methodology for studying flow dynamics in 3D in vitro vessel networks, enhancing our understanding of vascular physiology and pathology. TRANSLATIONAL IMPACT STATEMENT: This study introduces a new approach to modeling and flow assessment in 3D microvascular beds and surrounding interstitial spaces. Modeling interstitial space and endothelial monolayer thickness is essential for capturing fluid leakage from the microvascular network into the interstitial space and vice versa when the endothelial monolayer permeability is significantly affected in pathological conditions. Our approach to modeling 3D vascular networks can be used in vivo and in clinical settings to understand flow in tissue microvasculature and its surroundings under disease and healthy conditions.