Silicon nitride (Si3N4) is known to offer the required adhesion to chemically vapor deposited diamond coatings for demanding mechanical solicitations but the nature of their strong interface is not well know. Focused ion beam preparation preserved such thin layer for high resolution transmission electron microscopy. Contrarily to earlier suppositions, SiC interlinking particles were not found. Instead, the interface shows diamondlike carbon interlayers (approximately 3nm in thickness) intercalated with regions of directly-grown nanomicrometric and submicrometric-diamond crystals. A grain-to-grain epitaxial relationship of the type ⟨111⟩Dia∥⟨010⟩Si3N4 and {111}Dia∥{1¯20}Si3N4 is observed, concomitant with a 7:1 match arrangement, which assists on the interface strength.