Domain adaptation aims to mitigate performance degradation caused by distribution shifts between a labeled source domain and an unlabeled or sparsely labeled target domain. Most existing approaches estimate domain discrepancy either in feature space or in prediction space. However, these single-perspective strategies overlook a critical problem under domain shift: the reliability of the signals used for alignment. In practice, both learned representations and semantic predictions may become unreliable, and treating all target samples equally can lead to misleading alignment and suboptimal transfer. We introduce trust-aware domain adaptation, a principled framework that models domain discrepancy through the reliability of feature and prediction signals. Central to our approach is the Joint Feature-Prediction Discrepancy (JFPD), a unified formulation that jointly captures representation divergence and prediction divergence while weighting their contributions by sample-specific trust. Trust is quantified via two complementary mechanisms: uncertainty-aware trust, derived from prediction entropy to suppress unreliable predictions, and semantic-alignment trust, computed from prototype similarity in feature space to emphasize well-aligned representations. By prioritizing confident and semantically consistent samples while down-weighting noisy or ambiguous ones, JFPD provides a reliability-aware estimate of domain discrepancy. We further integrate JFPD into a training objective that guides adaptation toward trustworthy regions of the target domain. Experiments on standard benchmarks demonstrate that the proposed framework consistently achieves superior adaptation performance and yields discrepancy estimates that correlate with target-domain error. This work addresses, for the first time, the importance of modeling trust in the interaction between features and predictions for domain adaptation.