The interfacial Dzyaloshinkii-Moriya interaction defines a rotational sense for the spin structure in two-dimensional magnetic films and can be used to create chiral magnetic structures like spin spirals and skyrmions in those films. Here, we show by means of atomistic calculations that in heterostructures an interlayer coupling of the Dzyaloshinskii-Moriya type across a spacer can emerge. We quantify this interaction in the framework of the Lévy-Fert model for trilayers consisting of two ferromagnets separated by a nonmagnetic spacer and show that such an interlayer Dzyaloshinkii-Moriya interaction yields nontrivial three-dimensional spin textures across the entire trilayer, which evolve within as well as between the planes and, hence, combine intraplane and interplane chiralities. This analysis opens new perspectives for three-dimensional tailoring of magnetic chirality in multilayers.