This work studies linear coupled differential-difference systems, in the general case of multiple time-varying delays. The paper presents two main contributions: first, we formulate necessary and sufficient conditions for both the positivity and delay-independent asymptotic stability of this class of systems. Then, exploiting the Internally Positive Representation technique, we show how such stability results can be systematically exported to arbitrary (i.e. not necessarily positive) systems of the same class, providing a novel explicit sufficient condition for their delay-independent stability. The theoretical results are illustrated by a numerical example.