Multiscale modeling has become one of the dominant trends in solid mechanics and its neighboring fields over recent decades, opening new avenues and showing great potential for understanding and solving pressing engineering problems. At the same time, important questions arise on the theoretical foundations of scale transitions, in particular so concerning the partially overlapping realms of force field-based molecular mechanics and its coarse-grained variants on the one hand, and of homogenization theory within continuum mechanics on the other hand. Aiming at contributing to a better understanding of the theoretical pillars of multiscale mechanics, we will trace back both the stress average rule and the virial stress concept to the principle of virtual power, and provide a general semi-analytical frame for stress and strain up and downscaling in complex composites, along with application examples ranging from DNA to biocomposites.