In isolating languages such as Vietnamese, core morphological structure is encoded not by inflection but by the composition and ordering of monosyllabic morphemes, yet standard Transformer encoders largely overlook this signal. We introduce HuTieuBERT, a morpheme-aware Transformer that augments a pretrained Vietnamese encoder with two lightweight inductive biases: (i) Adaptive Boundary-Token Fusion, which integrates BMES-based morpheme boundary embeddings into token representations via a learnable gate, and (ii) a Morpheme-Aware Attention Bias, which injects a fixed structural attention matrix into early self-attention layers while minimally perturbing the pretrained attention geometry. Across a suite of Vietnamese POS, NER, and sentence-level classification benchmarks, HuTieuBERT consistently outperforms strong baselines, with the largest gains on syntactic tasks. Hyperparameter ablations show a broad regime in which structural biases improve accuracy without destabilizing representations. Applying the same design to ChineseBERT (Chinese-BERT-wwm) yields MAChineseBERT, which improves F₁ and produces more balanced tag distributions on Chinese POS and NER, suggesting that explicit morpheme-aware attention is a portable and effective strategy for modeling isolating languages.