Vascularisation is a critical factor in large-scale tissue engineering, as it supports the survival of cells in large tissue constructs. In native tissue, a hierarchical vascular network is present where larger vessels transport nutrients and oxygen throughout the body, and smaller capillaries facilitate blood-tissue exchange. In large-scale engineered tissue, such a functional hierarchical vascular network is necessary for cell survival. In this study, we aimed to create a high-density capillary network using biocompatible hydrogels for tissue engineering purposes. To achieve this, we first synthesised alginate-tyramine (ATA) by modifying the alginate backbone to contain tyramine groups. Then, we created monodisperse ATA microgels through in-air microfluidics (IAMF). These microgels were in turn used to form a microporous annealed particle (MAP) structure through photocrosslinking, which resulted in a structure containing the desired high-density microporous network. Next, we showed that we could use embedded 3D (emb3D) printing techniques to fabricate channels in the ATA hydrogel, which we stabilised through photocrosslinking. These macroscale channels proved to be open and perfusable. To create a stable interface between the microgels and hydrogel, we pre-saturated the microgels with a polymeric solution that forms an aqueous two-phase system (ATPS) with the ATA hydrogel. The ATPS and pre-saturation successfully counteracted capillary forces, keeping the hydrogel outside the microgel compartment. At the same time, the ATPS allowed the hydrogel and microgels to be in contact with each other, at which interface photocrosslinking was allowed to establish a connected structure. By combining these approaches, we were able to successfully assemble a perfusable hierarchical porous network with micro- and macroscale vasculature. Specifically, we fabricated a macroscale channel using emb3D printing methods in a bath with both hydrogel and microgel components, which we then solidified through photocrosslinking. The resulting MAP was perfused through the macroscale inlet with fluorescent particles, demonstrating successful perfusion through the printed channel. To date, the fabrication and perfusion of a multiscale vascular tree have not been demonstrated in this manner. Our study demonstrates the possibility for multiscale vascular emb3D printing through a microporous bath and highlights the potential of this innovative approach to overcome current limitations in tissue engineering.