A new difference-frequency method based on electro-optic phase modulators (EOMs) and two free-running lasers is reported to perform chirped-pulse dual-comb spectroscopy in the THz region. A variation of a near-IR interleaving scheme we recently reported has been developed to interleave the EOMs' orders and sidebands and to map THz comb teeth into the radio-frequency region below 1MHz. The down-converted comb teeth are shown to have transform limited widths of 1Hz over a 1s time scale. The dual chirp-pulsed scheme is used to measure the complex line shapes of two water vapor lines below 600GHz and to temporally magnify the effects of rapid passage by more than 60 000. For the 11,0 ← 10,1 transition in H2O, a pressure dependent phase perturbation is observed in the rapid passage response over the magnified time scale in contrast to a uniform line shape transformation observed for the 21,1 ← 20,2 transition of D2O. The possible origins for this anomalous behavior are modeled and discussed. The method is applicable to any region where difference or sum frequency waves can be generated.