All is relative. So what orbits about what is ambiguous with out defining criteria for what orbits what. For example, we might decide on the basis of sun wobble or not to a distant observer.

When our astronomers detect star wobble, they say that the star is orbiting about a massive companion planet or brown dwarf or a black hole.

Our sun is so massive compared to any planet, that it would not appear to wobble to a distant observer. Thus such distant astronomers would say that the planets in our solar system orbit around our sun. On this basis we can say the the moon orbits around the earth as earth wobble is not detectable, except on earth by way of the ocean tides
Wanda