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Diamond–graphene interfaces with admixtures of sp2- and sp3-hybridized bonds have been drawing increasing attention because of their potential for applications in electronic devices. In this work we investigate the formation of sp2-bonded domains included within sp3-bonded diamond structures, more specifically at 23 different low-energy diamond grain boundaries with 21 distinct surface orientations. To this end, we rely on an efficient constrained global-structure prediction algorithm, using energy and forces from density-functional theory and density-functional tight-binding, to identify low-energy interface reconstructions at grain boundaries. Our extensive simulations show that graphitic networks always stem from flattening and reconstruction of corrugated hexagonal layers with (111) orientation. The most stable sp2 insertions are found between parallel diamond surfaces. When these surfaces contain a ⟨110⟩ axis, we distinguish two classes of recurring reconstructions, while only one type is observed for diamond surfaces containing a ⟨100⟩ axis. We also study mixed sp2- and sp3-bonds as insertions at tilt grain boundaries, where bond distortion and bending of the graphitic planes, constrained by the grain geometry, have destabilizing effects. Finally, we study the electronic properties of these structures. While graphene adsorbed on diamond has usually a finite band gap, mixed diamond–graphene phases are mostly metallic, with localized states at the edges of the graphene-like stripes.