Broadband atmospheric phase spectra are acquired with a phase-sensitive dual-frequency-comb spectrometer by implementing adaptive compensation for the strong decoherence from atmospheric turbulence. The compensation is possible due to the pistonlike behavior of turbulence across a single spatial-mode path combined with the intrinsic frequency stability and high sampling speed associated with dual-comb spectroscopy. The atmospheric phase spectrum is measured across 2 km of air at each of the 70 000 comb teeth spanning across hundreds of near-infrared rovibrational resonances of , , and with submilliradian uncertainty, corresponding to a refractive index sensitivity. Trace gas concentrations extracted directly from the phase spectrum reach 0.7 ppm uncertainty, demonstrated here for . While conventional broadband spectroscopy only measures intensity absorption, this approach enables measurement of the full complex susceptibility even in practical open path sensing.