We present results from multifrequency polarization-sensitive Very Large Array observations of the Seyfert-starburst composite galaxy NGC 3079. Our sensitive radio observations reveal a plethora of radio "filaments" comprising the radio lobes in this galaxy. We analyze the origin of these radio filaments in the context of existing Chandra X-ray and HST emission-line data. We do not find a one-to-one correlation of the radio filaments with the emission-line filaments. The northeastern lobe is highly polarized with polarization fractions ∼33% at 5 GHz. The magnetic fields are aligned with the linear extents of the optically thin filaments, as observed in our, as well as other, observations in the literature. Our rotation measure images show evidence for rotation measure inversion in the northeastern lobe. Our data best fit a model where the cosmic rays follow the magnetic field lines generated as a result of the dynamo mechanism. There could be additional effects like shock acceleration that might also be playing a role. We speculate that the peculiar radio lobe morphology is a result of an interplay between both the superwinds and the active galactic nucleus jet that are present in the galaxy. The jet, in fact, might be playing a major role in providing the relativistic electron population that is present in the radio lobes.