Steganography is the art of hiding secret data into the cover media for covert communication. In recent years, more and more deep neural network (DNN)-based steganographic schemes are proposed to train steganographic networks for secret embedding and recovery, which are shown to be promising. Compared with the handcrafted steganographic tools, steganographic networks tend to be large in size. It raises concerns on how to imperceptibly and effectively transmit these networks to the sender and receiver to facilitate the covert communication. To address this issue, we propose in this paper a Purified and Unified Steganographic Network (PUSNet). It performs an ordinary machine learning task in a purified network, which could be triggered into steganographic networks for secret embedding or recovery using different keys. We formulate the construction of the PUSNet into a sparse weight filling problem to flexibly switch between the purified and steganographic networks. We further instantiate our PUSNet as an image denoising network with two steganographic networks concealed for secret image embedding and recovery. Comprehensive experiments demonstrate that our PUSNet achieves good performance on secret image embedding, secret image recovery, and image denoising in a single architecture. It is also shown to be capable of imperceptibly carrying the steganographic networks in a purified network.