Oxidized individual single-walled carbon nanotubes and amine polymers have been assembled into 11-32-nm-thick well-ordered conductive films. The films show highly anisotropic electrical conductivity, which is dominated by the nanotubes in the horizontal plane and by polymer-mediated tunneling in the vertical direction. The ratio of the "along" to "across" conductivity is similar to10(3). The subnanometer thick polymer layers interleaved with monolayers of nanotubes show conductivity several orders of magnitude higher than films of pristine polymers.