Exemplifying the advantages of microstructural design, heterogeneous materials have garnered increasing interest for their tailorable properties, such as high strength-to-weight ratios and enhanced corrosion resistance and durability. However, the inherently high-dimensional and morphologically diverse nature of microstructures makes unified parameterization nontrivial, fundamentally hindering accurate learning of microstructure–property relationships, particularly when the target mechanical response is strongly nonlinear and history-dependent under complex loading paths. To address this limitation, we develop a transferable latent-temporal learning model capable of end-to-end surrogate modelling of path-dependent nonlinear mechanical responses across diverse two-phase microstructures. The framework integrates (i) a latent representation module that autonomously extracts morphology-aware features from high-dimensional microstructural images and maps them into a compact latent space, and (ii) a temporal prediction module that encodes strain-path history to generate corresponding stress evolution. This coupled design avoids hand-crafted descriptors and enables efficient learning of the joint effects of morphology and loading history. Comprehensive numerical studies show that the proposed model achieves high predictive accuracy for in-distribution microstructures and, critically, maintains robust generalization and transferability to distinct microstructural representations and previously unseen loading paths. Moreover, the surrogate supports rapid inference, enabling fast nonlinear temporal simulations for morphologies and loading conditions beyond the training regime. Collectively, these results highlight a physics-guided, data-driven paradigm that improves generalization and interpretability in microstructure-conditioned constitutive modelling, thereby accelerating multiscale simulation and performance-driven design for heterogeneous materials.