High security and effectiveness are critical performance metrics in the data transmission process for satellite remote sensing images, medical images, and so on. Previously, the receiver could gain a high-quality cover image (lossy) after decryption in a separable manner to balance embedding capacity (EC) and security. Completely separable, reversible data hiding in encrypted image (SRDH-EI) algorithms are proposed to address this issue. In this study, the cover image was preprocessed at the sender’s end. The pre-embedded pixels and most significant bits (MSB) were compressed via two coding methods to reserve space. Additionally, the header data were embedded for marking. Finally, auxiliary data and secret data were embedded in a forward “Z” and reverse “Z” shape before and after encryption, respectively. The receiver could extract secret data and decrypt the cover image separately using the keys and markers. The experimental results demonstrate that the algorithm reached a high EC for remote sensing images by utilizing pixel correlation at multiple positions within the groups. The cover image could maintain its entropy during the data embedding process, ensuring security. The decrypted image could be recovered without distortion, furthermore, the receiver could achieve complete separability, so it has good application prospects for remote sensing images.