Although thermally conductive graphene sheets are efficient in enhancing in-plane thermal conductivities of polymers, the resulting nanocomposites usually exhibit low through-plane thermal conductivities, limiting their application as thermal interface materials. Herein, lamellar-structured polyamic acid salt/graphene oxide (PAAS/GO) hybrid aerogels are constructed by bidirectional freezing of PAAS/GO suspension followed by lyophilization. Subsequently, PAAS monomers are polymerized to polyimide (PI), while GO is converted to thermally reduced graphene oxide (RGO) during thermal annealing at 300 °C. Final graphitization at 2800 °C converts PI to graphitized carbon with the inductive effect of RGO, and simultaneously, RGO is thermally reduced and healed to high-quality graphene. Consequently, lamellar-structured graphene aerogels with superior through-plane thermal conduction capacity are fabricated for the first time, and its superior through-plane thermal conduction capacity results from its vertically aligned and closely stacked high-quality graphene lamellae. After vacuum-assisted impregnation with epoxy, the resultant epoxy composite with 2.30 vol% of graphene exhibits an outstanding through-plane thermal conductivity of as high as 20.0 W m−1 K−1, 100 times of that of epoxy, with a record-high specific thermal conductivity enhancement of 4310%. Furthermore, the lamellar-structured graphene aerogel endows epoxy with a high fracture toughness, ~ 1.71 times of that of epoxy.