I understand that a normal map imitates height/depht in all directions and height maps only in one. But in what situation would you ever wan to use both?
It's not super common, but it can be useful sometimes because a normal map doesn't have height information at all - just angle information. It can tell how sloped a surface is, which usually is enough to imitate the appearance of depth, but there's no way to get actual depth data from it. Similarly, there's no way to get actual angle information from a height or bump map. A conversion from one to the other is lossy by definition. It's usually close enough though.
It could also be useful just for adding procedural noise to an existing normal map or something for customization.