Several methods have been developed for generating 3D, in vitro, organ-on-chip models of human vasculature to study vascular function, transport, and tissue engineering. However, many of these existing models lack the hierarchical nature of the arterial-to-capillary-to-venous architecture that is key to capturing a more comprehensive view of the human microvasculature. Here, we present a perfusable, multi-compartmental model that recapitulates the three microvascular compartments to assess various physiological properties such as vessel permeability, vasoconstriction dynamics, and circulating cell arrest and extravasation. Viscous finger patterning and passive pumping create the larger arterial and venular lumens, while the smaller diameter capillary bed vessels are generated through self-assembly. These compartments anastomose and form a perfusable, hierarchical system that portrays the directionality of blood flow through the microvasculature. The addition of collagen channels reduces the apparent permeability of the central capillary region, likely by reducing leakage from the side channels, enabling more accurate measurements of vascular permeability-an important motivation for this study. Furthermore, the model permits modulation of fluid flow and shear stress conditions throughout the system by using hydrostatic pressure heads to apply pressure differentials across either the arteriole or the capillary. This is a pertinent system for modeling circulating tumor or T cell dissemination and extravasation. Circulating cells were found to arrest in areas conducive to physical trapping or areas with the least amount of shear stress, consistent with hemodynamic or mechanical theories of metastasis. Overall, this model captures more features of human microvascular beds and is capable of testing a broad variety of hypotheses.