Dual optical frequency comb spectroscopy allows for high speed, broadband measurements without any moving parts. Here, we combine differential chirp downconversion to probe large spectral bandwidths and serrodyne modulation to separate the positive and negative sidebands in a single modulator. As an initial demonstration, we apply this approach to measure a sharp cavity resonance to illustrate the system performance. We then measure methane transitions in the near-infrared and compare the resulting spectra to models based upon the current spectroscopic databases. The serrodyne method has lower hardware requirements compared to many existing approaches, and its simplicity enables a high degree of mutual coherence between the two combs. Further, this method is readily amenable to chip-scale photonic integration.