Transparent and conductive films (TCFs) are of great technological importance. Their high transmittance, electrical conductivity, and mechanical strength make single-walled carbon nanotubes (SWCNTs) a good candidate for the raw material for TCFs. Despite the ballistic transport in individual SWCNTs, electrical conductivity of SWCNT networks is limited by low efficiency of charge tunneling between the tube elements. Here, we demonstrate that the nanotube network sheet resistance at high optical transmittance is decreased by more than 50% when fabricated on graphene. This is a comparable improvement as that obtained through gold chloride (AuCl) doping. However, while Raman spectroscopy reveals substantial changes in spectral features of AuCl doped nanotubes, this does not occur with graphene. Instead, temperature-dependent transport measurements indicate that a graphene substrate reduces the tunneling barrier heights, while its parallel conductivity contribution is almost negligible. Finally, we show that combining the graphene substrate and AuCl doping, brings the SWCNT thin film sheet resistance down to 36 Ω/□.