Biomaterials are engaged ubiquitously to regenerate or replace damaged or diseased tissues. Numerous processing techniques aim to impart interconnected, porous structures within biomaterials to support cell delivery, direct tissue growth, and increase the acceptance of foreign materials in the body. Many processing techniques lack predictable control of scaffold architecture, and rapid prototyping methods are often limited by time-consuming, layer-by-layer fabrication of micro-features appropriate for biomaterials applications. Further, scaffold architecture is implicated in the body’s innate ability to isolate foreign substances making mitigation of this foreign body response (FBR) essential to ensuring the longevity of implanted biomaterials and devices. Bicontinuous interfacially jammed emulsion gels (bijels) offer a robust, self-assembly-based platform for synthesizing a new class of morphologically distinct biomaterials. Bijels form via kinetic arrest of temperature-driven spinodal decomposition in partially miscible binary liquid systems. These non-equilibrium soft materials comprise co-continuous, fully percolating, non-constricting liquid domains separated by a nanoparticle monolayer. In this dissertation, fluid incompatibility in bijels is exploited to process biocompatible precursors to form hydrogel scaffolds displaying the morphological characteristics of the parent bijel template. Bijel-derived materials are first used to generate structurally unique, fibrin-loaded polyethylene glycol hydrogel composites to demonstrate a new, robust cell delivery system. Next, bijel-derived materials are investigated as tissue integrating implants with high vascularization and FBR mitigation potential stemming from their uniquely arranged pore morphology, presenting a new paradigm for designing long-lasting biomaterials.