Thyroid nodule classification and segmentation in ultrasound images are crucial for computer-aided diagnosis; however, they face limitations owing to insufficient labeled data. In this study, we proposed a multi-view contrastive self-supervised method to improve thyroid nodule classification and segmentation performance with limited manual labels. Our method aligns the transverse and longitudinal views of the same nodule, thereby enabling the model to focus more on the nodule area. We designed an adaptive loss function that eliminates the limitations of the paired data. Additionally, we adopted a two-stage pre-training to exploit the pre-training on ImageNet and thyroid ultrasound images. Extensive experiments were conducted on a large-scale dataset collected from multiple centers. The results showed that the proposed method significantly improves nodule classification and segmentation performance with limited manual labels and outperforms state-of-the-art self-supervised methods. The two-stage pre-training also significantly exceeded ImageNet pre-training.