Controlling thermal anisotropy structure is important for emerging heat management applications such as thermal shield, thermal camouflage, and heat concentration. In this work, alternating stack epoxy composites (AECs) are prepared, inspired by the multilayer structure of an onion. Hexagonal boron nitride (h-BN) and expanded vermiculite (E-ver) are used as fillers in epoxy resin (Epon), taking as heat-dissipation layers and heat-insulation layers, respectively. Vertical heat isolation and local hotspot protection are endowed by the effective structural design. The temperature rise time of top surface is delayed by 404.2%, and the stabilized temperature is reduced by 10-15 degrees C (the bottom is heated to 120 degrees C); meanwhile, the whole composites are heated to 80 degrees C with good heat-dissipation performance, compared with those of homogeneous materials. There are two thermal phenomena synergistically in the anisotropy structure: excellent thermal protection when heating and good heat dissipation when cooling. Further, a thermal transfer mechanism of heat insulation and heat dissipation is analyzed based on numerical simulation and experiment. The multilayer epoxy composites are promising for the development of high-performance thermal products such as heat spreader, equipment cooling, and thermal hose.