In this work, we demonstrate yet another approach to tackle the amodal segmentation problem. Specifically, we first introduce a new representation, namely a semantics-aware distance map (sem-dist map), to serve as our target for amodal segmentation instead of the commonly used masks and heatmaps. The sem-dist map is a kind of level-set representation, of which the different regions of an object are placed into different levels on the map according to their visibility. It is a natural extension of masks and heatmaps, where modal, amodal segmentation, as well as depth order information, are all well-described. Then we also introduce a novel convolutional neural network (CNN) architecture, which we refer to as semantic layering network, to estimate sem-dist maps layer by layer, from the global-level to the instance-level, for all objects in an image. Extensive experiments on the COCOA and D2SA datasets have demonstrated that our framework can predict amodal segmentation, occlusion and depth order with state-of-the-art performance.