In this work, covalently bonded graphene/carbon nanotube (Gr/CNT) conjoined materials are fabricated as engineered three-dimensional hybrid multilayer supercapacitors for high-performance integrated electrochemical energy storage. Stable aqueous dispersion of polymer-modified graphene sheets are prepared in the presence of cationic poly(ethyleneimine), PEI (PEI-Gr) for sequential or electrostatic layer-by-layer (E-LBL) self-assembly with negatively charged acid-oxidized or functionalized multi-walled CNT (fMWCNT), forming (PEI-Gr/fMWCNT)n architecture as "all carbon" super-capacitor, where n = 1, 2, 4, 6, 9, 12 and 15. These films possess an interconnected network of mesoporous nanocarbon structure with well-defined interfaces allowing sufficient surface adsorption and faster ion transport due to short diffusion distances. They exhibit nearly rectangular cyclic voltammograms at an exceedingly high scan rate of 1 V/s with an average specific capacitance of -450 F g(-1) and specific energy density of 75.5 Wh kg(-1) based on electrode weight, measured at a current density of 0.3 A g(-1), comparable to that of Ni metal hydride battery and charged/discharged within a few seconds or a minute. This is attributed to the maximized synergistic effect of the highest specific surface areas by preventing re-aggregation of PEI-Gr or PEI-rGO via fMWCNT as spacers. We also determined relative contributions of the interfacial capacitance (C(dl)) and charge transfer (R(ct)) properties of the hybrids and investigated interfacial properties by SECM technique.