Overcoming sticky problems of large dielectric loss and poor breakdown strength ( Eb) is prerequisite of actual applications for high dielectric constant polymer composites. Herein, three kinds of multi-layer structure composites with different spatial structures (2MP-CE/CNT, CE/CNT-2MP-CE/CNT, MP-CE/CNT-MP) were prepared based on carbon nanotubes (CNTs), cyanate ester (CE) resin and mica paper (MP). Compared with traditional single-layer CE/CNT composite, multi-layer CE/CNT-2MP-CE/CNT composites, of which the middle layer is two pieces of MPs with a thickness of 60 µm, while both bottom and top layers are CE/CNT composite, simultaneously achieve 105 reduction in dielectric loss and 18.1 times increase in energy storage density ( Ue). Through modulating two sheets of MPs and CE/CNT as top and bottom layer, respectively, 2MP-CE/CNT composite with 60 μm MPs has the largest breakdown strength ( Eb), its Eb and Ue are severally about 7.1 and 19.5 times of those of CE/CNT composite. The relationship and mechanism between spatial structure and integrated performance such as dielectric properties, Eb and Ue of composites were systematically investigated. The attractive integrated performances of CE/CNT-2MP-CE/CNT and 2MP-CE/CNT composites are attributed to their unique composition and spatial structures, which bring special micro-capacitance and interfacial polarization, and thus leading to outstanding performances. Therefore, this investigation provides a strategy for getting desirable performances through building composites with specific spatial structure.