Additive manufacturing via layer‐by‐layer adhesive bonding holds much promise for scalable manufacturing of tissue‐like constructs, specifically scaffolds with integrated vascular networks for tissue engineering applications. However, there remains a lack of effective adhesives capable of composite layer fusion without affecting the integrity of patterned features. Here, the use of silicon carbide is introduced as an effective adhesive to achieve strong bonding (0.39 ± 0.03 kPa) between hybrid hydrogel films composed of alginate and collagen. The techniques have allowed us to fabricate multilayered, heterogeneous constructs with embedded high‐resolution microchannels (150 µm–1 mm) that are precisely interspaced (500–600 µm). Hydrogel layers are effectively bonded with silicon carbide nanoparticles without blocking the hollow microchannels and high cell viability (90.61 ± 3.28%) is maintained within the scaffold. Nanosilica is also tested and found to cause clogging of smaller microchannels when used for interlayer bonding, but is successfully used to attach synthetic polymers (e.g., Tygon) to the hydrogels (32.5 ± 2.12 mN bond strength). This allows us to form inlet and outlet interconnections to the gel constructs. This ability to integrate hollow channel networks into bulk soft material structures for perfusion can be useful in 3D tissue engineering applications.