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One three-dimensional (3-D) carbon-based heterogeneous interconnect scheme, consisting of a couple of horizontal multilayer graphene transmission lines (MLG-TL) and vertical through silicon carbon nanotube bundle vias (TS-CNTBV), is proposed and investigated theoretically. For its realization, some metallic bumps are used to integrate MLG-TLs with TS-CNTBVs, and contact resistance among them are characterized and compared. The lumped-element circuit model of a couple of MLG-TLs is also combined with that of TS-CNTBVs, with anomalous skin effect treated in an appropriate way. Numerical studies are performed for capturing distributed parameters as well as transmission characteristics of MLG-TLs, TS-CNTBVs, and whole 3-D interconnects at different operating frequencies. It is believed that this study can provide some useful information about carbon-based heterogeneous interconnects, where both graphene and carbon nanotube advantages can be exploited for the future 3-D ICs.