Heterogeneous materials are ubiquitous in modern engineering applications, including composites, polycrystalline solids, and multifunctional materials, whose macroscopic responses are governed by complex interactions across multiple length scales. Accurate prediction of their effective behavior therefore requires multiscale modeling frameworks that rigorously bridge microscale physics and macroscale responses. While classical computational homogenization methods provide a solid theoretical foundation, their practical deployment is often hindered by prohibitive computational costs, particularly for high-resolution microstructures or nonlinear multiphysics problems. Deep Material Networks (DMNs) have recently emerged as efficient surrogate models for homogenization, offering orders-of-magnitude acceleration while preserving essential principles of homogenization theory. In this work, DMNs are re-examined from a geometric perspective, in which their hierarchical architecture is interpreted as a general homogenization operator acting on heterogeneous media. This reinterpretation elevates the DMN beyond a mechanical-specific surrogate model and establishes it as a unified homogenization framework that is independent of the underlying physical field. As a result, the framework naturally extends to a wide range of coupled physical phenomena, including mechanical, conductive, and piezoelectric responses. Numerical examples demonstrate the consistency of the proposed framework with direct numerical simulations (DNS), while highlighting its computational efficiency, flexibility, and suitability for multiscale and multiphysics modeling of heterogeneous materials.