Deep image steganography is a data hiding technology that conceal data in digital images via deep neural networks. However, existing deep image steganography methods only consider the visual similarity of container images to host images, and neglect the statistical security (stealthiness) of container images. Besides, they usually hides data limited to image type and thus relax the constraint of lossless extraction. In this paper, we address the above issues in a unified manner, and propose deep image steganography that can embed data with arbitrary types into images for secure data hiding and lossless data revealing. First, we formulate the data hiding as an image colorization problem, in which the data is binarized and further mapped into the color information for a gray-scale host image. Second, we design a conditional invertible neural network which uses gray-scale image as prior to guide the color generation and perform data hiding in a secure way. Finally, to achieve lossless data revealing, we present a multi-stage training scheme to manage the data loss due to rounding errors between hiding and revealing processes. Extensive experiments demonstrate that the proposed method can perform secure data hiding by generating realism color images and successfully resisting the detection of steganalysis. Moreover, we can achieve 100% revealing accuracy in different scenarios, indicating the practical utility of our steganography in the real-world.