With the increasing emphasis on security and privacy, video in the cloud sometimes needs to be stored and processed in an encrypted format. To facilitate the indexing and tampering detection of encrypted videos, data hiding is performed in encrypted videos. This paper proposes a novel separable scheme for encryption and reversible data hiding. In terms of encryption method, intra-prediction mode and motion vector difference are encrypted by XOR encryption, and quantized discrete cosine transform block is permutated based on logistic chaotic mapping. In terms of the reversible data hiding algorithm, difference expansion is applied in encrypted video for the first time in this paper. The encryption method and the data hiding algorithm are separable, and the embedded information can be accurately extracted in both encrypted video bitstream and decrypted video bitstream. The experimental results show that the proposed encryption method can resist sketch attack and has higher security than other schemes, keeping the bit rate unchanged. The embedding algorithm used in the proposed scheme can provide higher capacity in the video with lower quantization parameter and good visual quality of the labeled decrypted video, maintaining low bit rate variation. The video encryption and the reversible data hiding are separable and the scheme can be applied in more scenarios.