Watermarking as a traceable authentication technology has been widely applied in image copyright protection. However, most existing watermarking methods embed watermarks by adding irremovable perturbations to the cover image, causing permanent distortion. To address this issue, we propose a novel watermarking approach termed \textbf{C}over-\textbf{R}ecoverable Water\textbf{Mark} (CRMark). CRMark can losslessly recover the cover image and watermark in lossless channels and enables robust watermark extraction in lossy channels. CRMark leverages an integer Invertible Watermarking Network (iIWN) to achieve a lossless invertible mapping between the cover-image-watermark pair and the stego image. During the training phase, CRMark employs an encoder-noise-layer-decoder architecture to enhance its robustness against distortions. In the inference phase, CRMark first maps the cover-image-watermark pair into an overflowed stego image and a latent variable. Subsequently, the overflowed pixels and the latent variable are losslessly compressed into an auxiliary bitstream, which is then embedded into the clipped stego image using reversible data hiding. During extraction, in lossy channels, the noised stego image can directly undergo inverse mapping via iIWN to extract the watermark. In lossless channels, the latent variable and overflowed stego image are first recovered using reversible data hiding, followed by watermark extraction through iIWN. Extensive experimental results demonstrate that CRMark can be perfectly recovered in lossless channels while remaining robust to common distortions.