Traditional fibre-reinforced composite materials with excellent in-plane properties fare poorly when out-of-plane through-thickness properties are important. Composite architectures with fibres designed orthogonal to the two-dimensional (2D) layout in traditional composites could alleviate this weakness in the transverse direction, but all of the efforts so far have only produced limited success. Here, we unveil an approach to the 3D composite challenge, without altering the 2D stack design, on the basis of the concept of interlaminar carbon-nanotube forests that would provide enhanced multifunctional properties along the thickness direction. The carbon-nanotube forests allow the fastening of adjacent plies in the 3D composite. We grow multiwalled carbon nanotubes on the surface of micro-fibre fabric cloth layouts, normal to the fibre lengths, resulting in a 3D effect between plies under loading. These nanotube-coated fabric cloths serve as building blocks for the multilayered 3D composites, with the nanotube forests providing much-needed interlaminar strength and toughness under various loading conditions. For the fabricated 3D composites with nanotube forests, we demonstrate remarkable improvements in the interlaminar fracture toughness, hardness, delamination resistance, in-plane mechanical properties, damping, thermoelastic behaviour, and thermal and electrical conductivities making these structures truly multifunctional.