<p>With the widespread dissemination of digital media, the security of image data has attracted increasing attention. However, existing colour image meaningful ciphertext encryption schemes exhibit low ciphertext quality and poor reconstructed image quality. To address these issues, this paper proposes a colour image encryption scheme for meaningful ciphertext based on a two-dimensional coupled infinite collapsing chaotic mapping (2D-CICCM) and stairwise compression. First, the plaintext image is processed using stairwise compression followed by bit-level permutation to generate a noise-like ciphertext. The generated ciphertext is then embedded into a cover image to produce a meaningful ciphertext image. Unlike conventional compressive sensing methods, which usually neglect inter-channel redundancy in colour images, the proposed stairwise compression jointly exploits both spatial and inter-channel redundancies, thereby significantly improving the reconstruction quality of the decrypted image. Considering the Gaussian-like distribution of measurement values and the characteristics of GLSB-based embedding with correction, a histogram rearrangement and embedding-value adjustment strategy is further designed. This strategy minimises the distortion introduced to the cover image under given embedding constraints, leading to optimal meaningful ciphertext image quality. The pseudo-random sequences required in the encryption process are generated by the 2D-CICCM, which exhibits uniformly distributed attractors, relatively large Lyapunov exponents, and strong randomness, thus satisfying the requirements of cryptographic pseudo-random number generators. Experimental results demonstrate that the proposed scheme achieves favourable performance in terms of ciphertext quality, decryption accuracy, and security, validating its feasibility and effectiveness. The code is available at <a href="https://github.com/jsw1995/MCCIE_2D-CICCM">https://github.com/jsw1995/MCCIE_2D-CICCM</a>.</p>