Understanding nanoscale interactions at the interface between two media with different dielectric constants is crucial for controlling many environmental and biological processes, and for improving the efficiency of energy storage devices. In this contributed paper, we show that polarization effects due to such dielectric mismatch remarkably influence the double-layer structure of a polyelectrolyte solution confined between two charged surfaces. Surprisingly, the electrostatic potential across the adsorbed polyelectrolyte double layer at the confining surface is found to decrease with increasing surface charge density, indicative of a negative differential capacitance. Furthermore, in the presence of polarization effects, the electrostatic energy stored in the double-layer structure is enhanced with an increase in the charge amplification, which is the absorption of ions on a like-charged surface. We also find that all of the important double-layer properties, such as charge amplification, energy storage, and differential capacitance, strongly depend on the polyelectrolyte backbone flexibility and the solvent quality. These interesting behaviors are attributed to the interplay between the conformational entropy of the confined polyelectrolytes, the Coulombic interaction between the charged species, and the repulsion from the surfaces with lower dielectric constant.