In this paper, we prove several results on interleavings for persistent relative homology of sub-level sets, complexes and Rips complexes. To prove the relative interleavings for complexes and Rips complexes, we define a relative correspondence which is related to the Gromov-Hausdorff distance. We also apply the relative Rips interleaving to a coverage problem in sensor networks, and show that the interleaving captures some features about the sensors after perturbation from the information of the unperturbed system.