Battery health prediction is significant while challenging for intelligent battery management. This article proposes a general framework for both short-term and long-term predictions of battery health under unseen dynamic loading and temperature conditions using domain-adaptive multitask learning (MTL) with long-term regularization. First, features extracted from partial charging curves are utilized for short-term state of health predictions. Then, the long-term degradation trajectory is directly predicted by recursively using the predicted features within the multitask framework, enhancing the model integrity and lowering the complexity. Then, domain adaptation (DA) is adopted to reduce the discrepancies between different working conditions. Additionally, a long-term regularization is introduced to address the shortcoming that arises when the model is extrapolated recursively for future health predictions. Thus, the short-term prediction ability is maintained while the long-term prediction performance is enhanced. Finally, predictions are validated through aging experiments under various dynamic loading profiles. By using partial charging capacity-voltage data, the results show that the early-stage long-term predictions are accurate and stable under various working profiles, with root mean square errors below 2% and fitting coefficients surpassing 0.86.