Modeling the effective behavior of microstructured composites is a central topic in computational mechanics. Traditional homogenization methods include mean-field approaches, accurate yet approximate for linear behavior, and simulations on representative volume elements (RVEs), which handle more complex microstructures but are computationally expensive. Neural networks have emerged as an attractive alternative in this context, offering increased flexibility at a significantly reduced computational cost. We propose a physics-augmented neural network framework to learn the homogenized response of two-phase viscoelastic composites, explicitly conditioned on microstructural parameters. The model uses two Partially Input Convex Neural Networks (PICNNs), embedding generalized standard material (GSM) principles. By formulating the network in terms of invariants, isotropic behavior is enforced. Internal variables are automatically obtained by integrating the constitutive law over loading sequences. Microstructural descriptors, including phase volume fractions, phase properties, and features extracted via a neural network encoder, are incorporated into the input. This architecture captures the influence of microstructure on the homogenized behavior efficiently and consistently. Preliminary results use synthetic relaxation tests from a generalized Maxwell homogenization model. The network reproduces the macroscopic response while preserving physically consistent dissipation and internal variable evolution. It interpolates across different microstructures and phase properties, providing an efficient surrogate for costly RVE simulations. Comparisons with reference models are performed at material point and structural levels, deploying the learned constitutive law in finite element simulations via automatic code generation using the open-source MFront framework. Although the current study focuses on linear viscoelastic bi-phasic composites for comparison, the method extends to nonlinear behaviors and more complex microstructures. Ongoing work includes integrating additional microstructural descriptors and computing phase-wise statistical measures.