The intellectual property of deep networks can be easily "stolen" by surrogate model attack. There has been significant progress in protecting the model IP in classification tasks. However, little attention has been devoted to the protection of image processing models. By utilizing consistent invisible spatial watermarks, the work [1] first considered model watermarking for deep image processing networks and demonstrated its efficacy in many downstream tasks. Its success depends on the hypothesis that if a consistent watermark exists in all prediction outputs, that watermark will be learned into the attacker's surrogate model. However, when the attacker uses common data augmentation attacks (e.g., rotate, crop, and resize) during surrogate model training, it will fail because the underlying watermark consistency is destroyed. To mitigate this issue, we propose a new watermarking methodology, "structure consistency", based on which a new deep structure-aligned model watermarking algorithm is designed. Specifically, the embedded watermarks are designed to be aligned with physically consistent image structures, such as edges or semantic regions. Experiments demonstrate that our method is more robust than the baseline in resisting data augmentation attacks. Besides that, we test the generalization ability and robustness of our method to a broader range of adaptive attacks.