The human vasculature is essential in organs and tissues for the transport of nutrients, metabolic waste products, and the maintenance of homeostasis. The integration of vessels in in vitro organs-on-chip may, therefore, improve the similarity to the native organ microenvironment, ensuring proper physiological functions and reducing the gap between experimental research and clinical outcomes. This gap is particularly evident in drug testing and the use of vascularized models may provide more realistic insights into human responses to drugs in the pre-clinical phases of the drug development pipeline. In this context, different vascularized liver models have been developed to recapitulate the architecture of the hepatic sinusoid, exploiting either porous membranes or bioprinting techniques. In this work, we developed a method to generate perfusable vascular channels with a circular cross section within organs-on-chip without any interposing material between the parenchyma and the surrounding environment. Through this technique, vascularized liver sinusoid-on-chip systems with and without the inclusion of the space of Disse were designed and developed. The recapitulation of the Disse layer, therefore, a gap between hepatocytes and endothelial cells physiologically present in the native liver milieu, seems to enhance hepatic functionality (e.g., albumin production) compared to when hepatocytes are in close contact with endothelial cells. These findings pave the way to numerous further uses of microfluidic technologies coupled with vascularized tissue models (e.g., immune system perfusion) as well as the integration within multiorgan-on-chip settings.