Frequency combs present a unique tool for high-precision and rapid molecular spectroscopy. Difference frequency generation (DFG) of near-infrared sources is a common approach to generate passively stabilized mid-infrared combs. However, only little attention has been paid so far to precisely measure the coherence properties of such sources. Here, we investigate these using a Raman-soliton based DFG source driven by an Yb:fiber frequency comb. A heterodyne beat between the second harmonic of the phase-locked DFG comb near 4 µm and a 2 µm Tm:fiber frequency comb locked to the same optical reference is performed. Using this method, we measure the relative phase noise power spectral density of both combs. This results in a sub-Hz relative linewidth between the DFG comb and the Tm:fiber comb. We also introduce a new pump/seed delay locking mechanism based on interferometry for long-term stable intensity noise suppression.