We demonstrate a simple system for dual-comb spectroscopy based on two inherently coherent optical frequency combs generated via seeded parametric downconversion. The inbuilt coherence is established by making the two combs share a common comb line. We show that the inbuilt coherence makes it possible to use a simple numerical post-processing procedure to compensate for small drifts of the dual-comb interferogram arrival time and phase. This enables long-time coherent averaging of the interferograms.