The precise modeling of arbitrarily aligned different material interfaces in composite electromagnetic compatibility (EMC) applications, is introduced in this paper through a fully explicit family of three-dimensional weighted essentially nonoscillatory schemes in the time domain. Developing curvilinear tessellations of auxiliary nodes compliant with a convex combination of all optimal candidate stencils, the novel algorithm allocates pertinent weights for wide-band evaluations at the particular regions. Also, via an enhanced temporal integration, continuity conditions are imposed in a local regime, without any unfavorable instabilities or vector parasites. Thus, the prior volumetric concepts suppress intrinsic grid defects even when time-steps are fairly large unlike in usual approaches. Numerical analysis verifies these benefits by diverse realistic EMC structures with laborious interfaces of complex shapes, curvatures, and dissimilar media configurations