Three-dimensional porous architectures of graphene are desirable for energy storage, catalysis, and sensing applications. Yet it has proven challenging to devise scalable methods capable of producing co-continuous architectures and well-defined, uniform pore and ligament sizes at length scales relevant to applications. This is further complicated by processing temperatures necessary for high quality graphene. Here, bicontinuous interfacially jammed emulsion gels (bijels) are formed and processed into sacrificial porous Ni scaffolds for chemical vapor deposition to produce freestanding three-dimensional turbostratic graphene (bi-3DG) monoliths with high specific surface area. Scanning electron microscopy (SEM) images show that the bi-3DG monoliths inherit the unique microstructural characteristics of their bijel parents. Processing of the Ni templates strongly influences the resultant bi-3DG structures, enabling the formation of stacked graphene flakes or fewer-layer continuous films. Despite the multilayer nature, Raman spectra exhibit no discernable defect peak and large relative intensity for the Raman 2D mode, which is a characteristic of turbostratic graphene. Moiré patterns, observed in scanning tunneling microscopy images, further confirm the presence of turbostratic graphene. Nanoindentation of macroscopic pillars reveals a Young’s modulus of 30 MPa, one of the highest recorded for sp2 carbon in a porous structure. Overall, this work highlights the utility of a scalable self-assembly method towards porous high quality graphene constructs with tunable, uniform, and co-continuous microstructure.