We present a method for stylizing stereoscopic 3D images that guarantees consistency between the left and right views. Our method decomposes the left and right views of an input image into discretized disparity layers and merges the corresponding layers from the left and right views into a single layer where stylization takes place. We then construct new stylized left and right views by compositing portions of the stylized layers. Because the left and right views come from the same source layers, our method eliminates common artifacts that cause viewer discomfort. We also present a stereoscopic 3D painterly rendering algorithm tailored to our layer-based approach. This method uses disparity information to assist in stroke creation so that strokes follow surface geometry without ignoring painted surface patterns. Finally, we conduct a user study that demonstrates that our approach to stereoscopic 3D image stylization leads to images that are more comfortable to view than those created using other techniques.