Interfaces are crucial in natural and engineered systems, dictating essential biological, ecological, and technological properties that augment performance, functionality, and user experience. Yet, achieving precise interfacial control poses significant challenges in both conventional and additive manufacturing, where scalability constraints impede the controlled deposition of quasi-2D layers within 3D objects. This paper introduces Voxel-Interface 3D Printing (VI3DP), which enables comprehensive control over extruded voxel interfaces irrespective of the printhead diameter that conventionally dictates feature size. Various optical, mechanical, and electrical functionalizations, attaining interface thicknesses up to three orders of magnitude smaller than the voxel size are reported. Notable applications include encoding data in soft matter through fluorescent interfaces, creating tight fits and movable mechanisms through non-adhesive interfaces, fabricating bio-inspired composites with tailored failure modes, and developing a single filament capacitive touch sensor. VI3DP opens new avenues for enhanced functionality and efficiency across multiple fields, including biomedical technology, electronics, optics, andnanotechnology.