Context. The Vela complex is a region of the sky that gathers several stellar and interstellar structures in a few hundred square degrees. Aims.Gaia data now allow us to obtain a 3D view of the Vela interstellar structures through the dust extinction. Methods. We used the FEDReD (Field Extinction-Distance Relation Deconvolver) algorithm on near-infrared 2MASS data, cross-matched with the Gaia DR2 catalogue, to obtain a 3D cube of extinction density. We applied the FellWalker algorithm to this cube to locate clumps and dense structures. Results. We analysed 18 million stars over 450 deg² to obtain the extinction density of the Vela complex from 0.5 to 8 kpc at ℓ ∈ [250° ,280° ] and b ∈ [ − 10° ,5° ]. This cube reveals the complete morphology of known structures and relations between them. In particular, we show that the Vela Molecular Ridge is more likely composed of three substructures instead of four, as suggested by the 2D densities. These substructures form the shell of a large cavity. This cavity is visually aligned with the Vela supernova remnant but located at a greater distance. We provide a catalogue of location, distance, size, and total dust content of Interstellar Medium (ISM).