A method to measure and correct for spectral baseline fluctuations in dual-comb interferometry is presented. Fluctuations can be measured from the amplitude of beat notes between combs and a continuous wave laser or from a separate measurement of the combs' repetition rates, filtered around the spectral region of interest. Amplitude-dependent spectral variations are characterized using low-resolution Fourier transforms around the centerburst of several interferograms, and a nonstationary filter is applied to properly account for the combs' variations during the measurement. This allows removal of this source of statistical, as well as systematic, errors.