The dielectric relaxation dynamics in polymer composites critically determine their functional performance in advanced electrical systems. This study systematically investigates hybrid epoxy composites comprising neat epoxy resin (EP) and paper-reinforced systems (EIP), modified with 10–50 wt% polypropylene glycol diglycidyl ether (PEGDGE) plasticizer. Through synergistic application of differential scanning calorimetry (DSC) and broadband dielectric spectroscopy (10⁻¹–10⁶ Hz), the quantitative relationships between plasticizer content, glass transition temperature (Tg), and dielectric relaxation processes were established. DSC analysis reveals a linear Tg dependence with increasing PEGDGE content, attributed to enhanced molecular mobility. Dielectric characterization demonstrates three distinct relaxation regimes: α-relaxation below Tg, interfacial polarization at epoxy/PEGDGE boundaries, and paper/epoxy interfacial effects in EIP systems. A quantitative dielectric relaxation model was developed based on complex modulus formalism, coupled with Vogel–Fulcher–Tammann (VFT) analysis of DC conductivity. Activation energy mapping through Arrhenius decomposition reveals three characteristic values: (1) 82.01–87.80 kJ/mol for α-relaxation, (2) 55.96–64.64 kJ/mol for epoxy/PEGDGE interfaces, and (3) 30.88–44.38 kJ/mol for epoxy/paper interfaces. Crucially, the plasticizer content modulates these activation energies, demonstrating its role in tailoring interfacial dynamics.