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We characterize Galactic dust filaments by correlating BICEP/Keck and Planck data with polarization templates based on neutral hydrogen (Hi) observations. Dust polarization is important for both our understanding of astrophysical processes in the interstellar medium (ISM) and the search for primordial gravitational waves in the cosmic microwave background (CMB). In the diffuse ISM, Hiis strongly correlated with the dust and partly organized into filaments that are aligned with the local magnetic field. We analyze the deep BICEP/Keck data at 95, 150, and 220 GHz, over the low-column-density region of sky where BICEP/Keck has set the best limits on primordial gravitational waves. We separate the Hiemission into distinct velocity components and detect dust polarization correlated with the local Galactic Hibut not with the Hiassociated with Magellanic Streami. We present a robust, multifrequency detection of polarized dust emission correlated with the filamentary Himorphology template down to 95 GHz. For assessing its utility for foreground cleaning, we report that the Himorphology template correlates inBmodes at a ∼10%–65% level over the multipole range 20 <ℓ< 200 with the BICEP/Keck maps, which contain contributions from dust, CMB, and noise components. We measure the spectral index of the filamentary dust component spectral energy distribution to beβ= 1.54 ± 0.13. We find no evidence for decorrelation in this region between the filaments and the rest of the dust field or from the inclusion of dust associated with the intermediate velocity Hi. Finally, we explore the morphological parameter space in the Hi-based filamentary model.