The rheology of lyotropic cholesteric liquid crystalline phase forming double-stranded DNA (dsDNA) stabilized single-wall carbon nanotube (SWCNT) dispersions was analyzed over a wide range of SWCNT concentrations. In the semidilute regime, supernatant dispersions of dsDNA-SWCNTs showed the characteristic rheological behavior of semidilute solutions of rods predicted by the Doi-Edwards theory. These cholesterogenic liquid crystal dispersions exhibited some of the key rheological behaviors associated with lyotropic liquid crystalline polymers (LLCPs) including a non-monotonic relationship in the viscosity and moduli versus concentration curves, and the empirical Cox-Merz not being obeyed. However, the dsDNA-SWCNT viscosity versus shear rate curves exhibited an inflection point instead of the three distinct regions associated with many LLCPs and nanocylinder dispersions. This could be related to orientation defects and inherent secondary interactions between the dsDNA and the SWCNTs. Linear viscoelasticity measurements also showed similarities to other lyotropic systems.