Exploiting multiple physical layers for communications has gained increasing interest recently to improve reliability and/or coverage range. Powerline and unlicensed wireless communication networks are attractive candidates to realize this objective because of their ubiquity. However, their performance can be severely degraded by impulsive noise (IN) and narrowband interference (NBI), respectively. In this paper, we exploit the inherent sparse structures of NBI and IN in the frequency and time domains, respectively, to propose an efficient joint estimation and mitigation scheme based on compressive sensing (CS) principles. Moreover, we investigate the metric of maximum expected coherence of our scheme for realistic powerline communication (PLC) and wireless channels, which provides some insight into its performance. Finally, our numerical experiments demonstrate the superiority of jointly processing the wireless and PLC channel outputs for CS-based NBI and IN mitigation over separate processing of individual channel outputs.