Confocal microscopy and rheology studies of two bijel systems are presented to elucidate relationships between the physicochemical properties of bijels and their ability to be utilized as soft matter templates for materials synthesis. For the first time, the origins of viscoelasticity in these systems are investigated using conventional rheometry and a direct correspondence between the elastic storage modulus, particle loading, and the departure from criticality is observed. Further, the rheological transitions that accompany fluid re-mixing in bijels are characterized, providing key insights into the synergistic role of interfacial tension and interparticle interactions in mediating their mechanical robustness. Bijels that are predominantly stabilized by interfacial tension are also highly sensitive to gradients in chemical composition and more easily prone to mechanical failure during processing. Despite this increased sensitivity, a modified strategy for processing these more delicate systems is developed and its efficacy is demonstrated by synthesizing a bicontinuous macroporous hydrogel scaffold.