We use a resistive-pulse technique to analyze molecular hybrids of single-wall carbon nanotubes (SWNTs) wrapped in either single-stranded DNA or protein. Electric fields confined in a glass capillary nanopore allow us to probe the physical size and surface properties of molecular hybrids at the single-molecule level. We find that the translocation duration of a macromolecular hybrid is determined by its hydrodynamic size and solution mobility. The event current reveals the effects of ion exclusion by the rod-shaped hybrids and possible effects due to temporary polarization of the SWNT core. Our results pave the way to direct sensing of small DNA or protein molecules in a large unmodified solid-state nanopore by using nanofilaments as carriers.