The use of embedded cooling layers consisting of materials with high thermal conductivities can significantly reduce peak temperatures within solid-state heat-generating media. Inversely, such layers can also allow for increases in heat-generating densities for a given maximum peak temperature. This is applicable in, for instance, integrated passive power electronics, where power densities are limited by the low thermal conductivities of materials being used. In this paper, the thermal performance of embedded cooling layers in three-dimensional rectangular heat-generating components is investigated numerically for a boundary condition where heat escapes to the ambient in two orthogonal direction sets (sets of orthogonal positive and/or negative directions). The allowable increase in heat generation density for fixed maximum peak temperatures is described for a wide range of geometric shape conditions and thermal conductivities of materials present in such composite structures. Correlations were developed for conditions with and without significant thermal resistance at the internal interfaces of the material layers and externally between the composite component structure and the environment. Conventional one-dimensional and first-order approximations traditionally used in composite solid conduction problems can accurately account for neither the relative thickness of material layers, nor the impact that internal interfacial resistance has. This paper presents a method with which the peak temperature within a stacked sandwich structure containing embedded cooling layered and where heat is removed in two orthogonal direction sets can be determined without the use of a numerical package. The method was developed for a wide range of material properties, geometric sizes and interfacial resistance values.