Mispronunciation detection and diagnosis (MDD) is a popular research focus in computer-aided pronunciation training (CAPT) systems. End-to-end (e2e) approaches are becoming dominant in MDD. However an e2e MDD model usually requires entire speech utterances as input context, which leads to significant time latency especially for long paragraphs. We propose a streaming e2e MDD model called CoCA-MDD. We utilize conv-transformer structure to encode input speech in a streaming manner. A coupled cross-attention (CoCA) mechanism is proposed to integrate frame-level acoustic features with encoded reference linguistic features. CoCA also enables our model to perform mispronunciation classification with whole utterances. The proposed model allows system fusion between the streaming output and mispronunciation classification output for further performance enhancement. We evaluate CoCA-MDD on publicly available corpora. CoCA-MDD achieves F1 scores of 57.03% and 60.78% for streaming and fusion modes respectively on L2-ARCTIC. For phone-level pronunciation scoring, CoCA-MDD achieves 0.58 Pearson correlation coefficient (PCC) value on SpeechOcean762.