Image hiding is the study of techniques for covert storage and transmission, which embeds a secret image into a container image and generates stego image to make it similar in appearance to a normal image. However, existing image hiding methods have a serious problem that the hiding and revealing process cannot be fully invertible, which results in the revealing network not being able to recover the secret image losslessly, which makes it impossible to simultaneously achieve high fidelity and secure transmission of the secret image in an insecure network environment. To solve this problem,this paper proposes a fully invertible image hiding architecture based on invertible neural network,aiming to realize invertible hiding of secret images,which is invertible on both data and network. Based on this ingenious architecture, the method can withstand deep learning based image steganalysis. In addition, we propose a new method for enhancing the robustness of stego images after interference during transmission. Experiments demonstrate that the FIIH proposed in this paper significantly outperforms other state-of-the-art image hiding methods in hiding a single image, and also significantly outperforms other state-of-the-art methods in robustness and security.