Faraday tomography of polarimetric observations at low frequency in the radio is a unique tool for studying the structure of the magneto-ionic diffuse interstellar medium (ISM) based on Faraday depth. LOFAR data below 200 MHz have revealed a plethora of features in polarization, whose origin remains unknown. Previous studies have highlighted the remarkable association of such features with tracers of the magnetized-neutral ISM, such as interstellar dust and atomic hydrogen (HI). However, the physical conditions responsible for the correlation between magneto-ionic and neutral media have not been clarified yet. In this Letter we further investigate the correlation between LOFAR data and the HI spectroscopic observations at 21 cm from the Effelsberg-Bonn HI Survey (EBHIS). We focus on the multiphase properties of the HI gas. We present the first statistical study on the morphological correlation between LOFAR tomographic data and the cold (CNM), lukewarm (LNM), and warm (WNM) neutral medium HI phases. We use the Regularized Optimization for Hyper-Spectral Analysis approach to decompose the HI phases based on a Gaussian decomposition of the HI spectra. We study four fields of view – Fields 3C196, A, B, and C – and find, in at least the first two, a significant correlation between the LOFAR and EBHIS data using the histograms of oriented gradients (HOG) feature. The absence of a correlation in Fields B and C is caused by a low signal-to-noise ratio in polarization. The observed HOG correlation in Fields 3C196 and A is associated with all HI phases and it is surprisingly dominant in the CNM and LNM phases. We discuss possible mechanisms that would explain the correlation between CNM, LNM, and WNM with polarized emission at Faraday depths up to 10 rad m−2. Our results show how the complex structure of the ionic medium seen by the LOFAR tomographic data is tightly related to phase transition in the diffuse and magnetized neutral ISM traced by HI spectroscopic data.