This paper introduces the internally positive representation (IPR) of linear coupled differential-difference systems with time-varying delays. Then, a stability analysis is conducted on this class of systems: Relying on results established under positivity assumptions, the IPR technique leads to a novel sufficient condition for the delay-independent asymptotic stability of coupled differential-difference systems that holds for not necessarily positive systems. As a consequence, an analogous stability condition for neutral-type equations with time-varying delays is also obtained. The results are discussed and favorably compared to similar conditions proposed in the literature, and finally validated by means of numerical examples.