Unwrapping an image to a plane so it is mirrored on both sides

So, I’m working with making 2d characters for a game. I’m making meshes in Blender for them, and I’m making the models using planes and then unwrapping textures to those planes. However, I’d like them to be able to turn around in Unity by simply rotating the models (so they’ll turn into straight lines as the edge of the plane faces the camera, then they’ll come around and face the opposite way). Unfortunately, when I just unwrapped images using the UV editor, it came out in such a way that when viewed from the far side, the models are upside-down. Is there any clever way I can make it so that each side of the plane has the same version of the image, only facing opposite directions?