Ideal dielectric materials for microelectronic devices should have high directionally tailored thermoconductivity with low dielectric constant and loss. Hexagonal boron nitride (hBN) with excellent thermal and dielectric properties shows a promise for the fabrication of thermoconductive dielectric polymer composites. Herein, a simple method for the fabrication of lightweight polymer/hBN composites with high directionally tailored thermoconductivity and excellent dielectric properties is presented. The solid polymer/hBN composites are manufactured by melt-compounding and injection molding. The porous composites are successfully manufactured in an injection molding process through supercritical fluid (SCF) foaming. X-ray tomography provides direct visualization of the internal microstructure and hBN orientation, leading to an in-depth understanding of the directionally dependent thermoconductivity of the polymer/hBN composite. Shear-induced orientation of hBN platelets in the solid HDPE/hBN composites leads to a significant anisotropic thermal conductivity. The solid HDPE/23.2 vol % hBN composites show an in-plane thermoconductivity as high as 10.1 W m-1 K-1, whereas the through-plane thermoconductivity is limited to 0.28 W m-1 K-1. However, the generation of a porous structure via SCF foaming imparts in situ exfoliation, random orientation, and interconnectivity of hBN platelets within the polymer matrix. This results in highly isotropic thermoconductivity with higher bulk thermal conductivity in the lightweight porous composites as compared to their solid counterparts. Furthermore, the electrically insulating composites developed in this study exhibit low dielectric constant and ultralow dielectric loss. Thus, this study presents a simple fabrication method to develop lightweight dielectric materials with tailored thermal conductivity for modern electronics.