We demonstrate the precision molecular spectroscopy of H13CN using a free-running, all-fiber dual electro-optic frequency comb system. Successive interferograms, acquired at a rate of Δfrep=1 MHz, were phase-corrected in post-processing, averaged, and normalized to yield the complex transmission spectrum of several transitions within the 2ν1H13CN band centered near λ=1545 nm. With spectral signal-to-noise ratios as high as 326:1 achieved in 2 ms of integration time, we report accurate measurements of H13CN transition intensities which will aid in the study of extreme astrophysical environments.