The displacement- and frequency-noise-free interferometer (DFI) is a multiple laser interferometer array for gravitational-wave detection free from both the displacement noise of optics and laser frequency noise. So far, partial experimental demonstrations of the DFI have been done in 2D table top experiments. In this Letter, we report the complete demonstration of a 3D DFI. The DFI consists of four Mach-Zehnder interferometers with four mirrors and two beam splitters The attained maximum suppression of the displacement noise of both mirrors and beam splitters was 40 dB at about 50 MHz. The nonvanishing DFI response to a gravitational wave was successfully confirmed using multiple electro-optic modulators and computing methods.