Mergers are thought to be a fundamental channel for galaxy growth, perturbing the gas dynamics and the magnetic fields (B-fields) in the interstellar medium (ISM). However, the mechanisms that amplify and dissipate B-fields during a merger remain unclear. We characterize the morphology of the ordered B-fields in the multiphase ISM of the closest merger of two spiral galaxies, the Antennae galaxies. We compare the inferred B-fields using 154 μm thermal dust and 11 cm radio synchrotron emission polarimetric observations. We find that the 154 μm B-fields are more ordered across the Antennae galaxies than the 11 cm B-fields. The turbulent-to-ordered 154 μm B-field increases at the galaxy cores and star-forming regions. The relic spiral arm has an ordered spiral 154 μm B-field, while the 11 cm B-field is radial. The 154 μm B-field may be dominated by turbulent dynamos with high 12CO(1-0) velocity dispersion driven by star-forming regions, while the 11 cm B-field is cospatial with high H I velocity dispersion driven by galaxy interaction. This result shows the dissociation between the warm gas mainly disturbed by the merger, and the dense gas still following the dynamics of the relic spiral arm. We find a ~8.9 kpc scale ordered B-field connecting the two galaxies. The base of the tidal tail is cospatial with the H I and 12CO(1-0) emission and has compressed and/or sheared 154 μm and 11 cm B-fields driven by the merger. We suggest that amplified B-fields, with respect to the rest of the system and other spiral galaxies, may be supporting the gas flow between both galaxies and the tidal tail. * SALSA provides a software repository at https://github.com/galmagfields/hawc, and publicly available data at http://galmagfields.com/.