Change detection is a crucial technique in remote sensing image analysis and faces challenges such as background complexity and appearance shift, resulting in incomplete change boundaries and pseudo changes. This paper introduces a novel wavelet siamese network with semi-supervised domain adaptation to address these issues, named WS-Net++. WS-Net++ establishes spatial-frequency interactions between bitemporal images to enhance the completeness of the change boundaries. The spatial-domain interaction highlights the pixel-wise differences. The frequency-domain interaction firstly adaptively adjusts the contributions from different frequency components based on image context. Within-frequency and between-frequency interactions are further constructed to capture the frequency-domain differences, enabling the adaptive and effective handling of both overall and subtle changes. Additionally, WS-Net++ employs a semi-supervised domain adaptation strategy to mitigate the appearance shifts between bitemporal images. By categorizing regions into changed, unchanged, and regions of no interest in a semi-supervised manner, the network minimizes intra-class discrepancies within unchanged regions and maximizes inter-class discrepancies between changed regions, reducing the domain gap. Experimental results on the LEVIR-CD, WHU-CD, and CLCD datasets demonstrate that our WS-Net++ outperforms alternative methods, achieving F1 scores of 91.31%, 94.52%, and 79.77%, respectively. The code and models will be publicly available at https://github.com/JiTaiTai/WS-Net_Plus for reproducible research.