Depression detection from social media text is critical for early mental health intervention, yet existing NLP systems underperform in low-resource, code-mixed settings. Bangla-English code-mixing, common across South Asian online communities, poses unique challenges due to irregular grammar, transliteration, and scarce labeled data. To address this gap, we introduce DepressiveText, a 7,019-sample dataset of Bangla-English social media posts annotated for depressive signals, with strong inter-annotator agreement (𝜅 = 0.84). We further propose a hybrid architecture that combines BanglishBERT embeddings with an LSTM classifier, enabling the model to capture both contextual and sequential cues. Comparative experiments with traditional ML, deep learning, and multilingual transformer baselines demonstrate that our approach achieves the highest performance, with an accuracy of 0.8889. We also employ LIME to enhance interpretability by identifying key lexical triggers. Our findings underscore the effectiveness of hybrid transformer–sequence models for low-resource code-mixed NLP and highlight their potential in real-world mental health applications.