The aim of steganography detection is to identify whether the multimedia data contain hidden information. Although many detection algorithms have been presented to solve tasks with inconsistent distributions between the source and target domains, effectively exploiting transferable correlation information across domains remains challenging. As a solution, we present a novel multiperspective progressive structure adaptation (MPSA) scheme based on active progressive learning (APL) for JPEG steganography detection across domains. First, the source and target data originating from unprocessed steganalysis features are clustered together to explore the structures in different domains, where the intradomain and interdomain structures can be captured to provide adequate information for cross-domain steganography detection. Second, the structure vectors containing the global and local modalities are exploited to reduce nonlinear distribution discrepancy based on APL in the latent representation space. In this way, the signal-to-noise ratio (SNR) of a weak stego signal can be improved by selecting suitable objects and adjusting the learning sequence. Third, the structure adaptation across multiple domains is achieved by the constraints for iterative optimization to promote the discrimination and transferability of structure knowledge. In addition, a unified framework for single-source domain adaptation (SSDA) and multiple-source domain adaptation (MSDA) in mismatched steganalysis can enhance the model's capability to avoid a potential negative transfer. Extensive experiments on various benchmark cross-domain steganography detection tasks show the superiority of the proposed approach over the state-of-the-art methods.