  We study two notions of relative differential cohomology, using the model of
differential characters. The two notions arise from the two options to
construct relative homology, either by cycles of a quotient complex or of a
mapping cone complex. We discuss the relation of the two notions of relative
differential cohomology to each other. We discuss long exact sequences for both
notions, thereby clarifying their relation to absolute differential cohomology.
We construct the external and internal product of relative and absolute
characters and show that relative differential cohomology is a right module
over the absolute differential cohomology ring. Finally we construct fiber
integration and transgression for relative differential characters.
