The application of stress to multiphase solid-liquid systems often results in morphological instabilities. Here we propose a solid-solid phase transformation model for roughening instability in the interface between two porous materials with different porosities under normal compression stresses. This instability is triggered by a finite jump in the free energy density across the interface, and it leads to the formation of fingerlike structures aligned with the principal direction of compaction. The model is proposed as an explanation for the roughening of stylolites-irregular interfaces associated with the compaction of sedimentary rocks that fluctuate about a plane perpendicular to the principal direction of compaction.