We present a hybrid approach that combines top-down fabrication with bottom-up directed assembly for making single-walled carbon nanotube (SWNT) based three-dimensional interconnects. The SWNTs are assembled using dielectrophoresis at room temperature on a microfabricated 3D platform. The two-terminal resistance of the assembled SWNTs at 10 Vpp assembly voltage is approximately 545 Ω. Simulation of the dielectrophoretic assembly is carried out to understand the behavior of the SWNTs during assembly. Encapsulation of these devices using a conformal pinhole-free parylene layer resulted in a decrease of the total resistance.