Epoxy-based solid insulation is widely used in high-voltage systems; however, its breakdown reliability and thermal endurance remain critical limitations under coupled electrothermal stresses. This study investigates mesoporous Mg/Al hydrotalcite as a multifunctional nanofiller for enhancing the dielectric, breakdown, and thermal performance of epoxy insulation. Mesoporous Mg/Al-LDH nanoparticles were synthesized via a co-precipitation route and functionalized with 3-aminopropyltriethoxysilane (APTES) to improve filler dispersion and interfacial compatibility with epoxy. XRD, TEM/SAED, BET/BJH, and FTIR analyses confirmed the successful formation of layered hydrotalcite nanosheets with mesoporous characteristics and effective surface functionalization. The functionalized nanoparticles were incorporated into epoxy at loadings of 1–7 wt.% and evaluated using broadband dielectric spectroscopy, AC breakdown testing with Weibull statistical analysis, SEM/EDX mapping, TGA, DSC, and compressive strength. The results showed that Mg/Al-LDH incorporation maintained a moderate permittivity variation and a dielectric loss tangent below 0.01 at 50 Hz. The optimum 5 wt.% nanocomposite achieved an AC breakdown strength of 36.75 kV/mm, corresponding to a 22.2% improvement over neat epoxy, together with enhanced Weibull reliability. Thermal analysis showed that the degradation onset temperature increased from 341 °C to 357 °C, and the glass transition temperature improved by 22%. Compression testing showed an increase in the maximum recorded compressive stress from 103.9 MPa for neat epoxy to 128.7 MPa for the 5 wt.% nanocomposite, corresponding to approximately 23.9%; however, the different deformation and failure responses limit direct comparison of compressive strength. The findings demonstrate that APTES-functionalized mesoporous Mg/Al-LDH is a promising alternative to conventional oxide nanofillers for high-performance GIS/GITL insulation applications.