A method of creating a functionally-graded multi-material (FGM) part in multi-material additive manufacturing includes providing a part digitized into voxels, generating a lattice structure having a series of repeating unit cells, where each is the smallest nonrepeating constituent of the lattice structure and is generated by a continuous surface defined by a continuous function. The method further includes taking an inverse volume of the lattice structure within the part, creating a material gradient by varying a thickness of the surface at the boundary between the lattice structure and the inverse volume, assigning one of the two FGM component materials to the voxels in the volume occupied by the lattice structure and assigning the other to the voxels occupied by the inverse volume, outputting the voxels each with a designated material, the lattice structure and the inverse volume forming a mechanical interlock at the interface of the two component materials.