Despite the recent success of face image generation with GANs, conditional hair editing remains challenging due to the under-explored complexity of its geometry and appearance. In this paper, we present MichiGAN (Multi-InputConditioned Hair Image GAN), a novel conditional image generation method for interactive portrait hair manipulation. To provide user control over every major hair visual factor, we explicitly disentangle hair into four orthogonal attributes, including shape, structure, appearance, and background. For each of them, we design a corresponding condition module to represent, process, and convert user inputs, and modulate the image generation pipeline in ways that respect the natures of different visual attributes. All these condition modules are integrated with the backbone generator to form the final end-toend network, which allows fully-conditioned hair generation from multiple user inputs. Upon it, we also build an interactive portrait hair editing system that enables straightforward manipulation of hair by projecting intuitive and high-level user inputs such as painted masks, guiding strokes, or reference photos to well-defined condition representations. Through extensive experiments and evaluations, we demonstrate the superiority of our method regarding both result quality and user controllability.