Video portraits relighting is critical in user-facing human photography, especially for immersive VR/AR experience. Recent advances still fail to recover consistent relit result under dynamic illuminations from monocular RGB stream, suffering from the lack of video consistency supervision. In this paper, we propose a neural approach for real-time, high-quality and coherent video portrait relighting, which jointly models the semantic, temporal and lighting consistency using a new dynamic OLAT dataset. We propose a hybrid structure and lighting disentanglement in an encoder-decoder architecture, which combines a multi-task and adversarial training strategy for semantic-aware consistency modeling. We adopt a temporal modeling scheme via flow-based supervision to encode the conjugated temporal consistency in a cross manner. We also propose a lighting sampling strategy to model the illumination consistency and mutation for natural portrait light manipulation in real-world. Extensive experiments demonstrate the effectiveness of our approach for consistent video portrait light-editing and relighting, even using mobile computing.