Dual Monarchy

Dual Monarchy is when a monarch or an royal family rules over two or more sovereign states, where each of the states have its own trade bloc and combines its military, even though each state rules itself. The powers of the monarch can be limited or absolute.

History
The most famous dual monarchy in history was the Austro-Hungarian Empire, formed with the Austro-Hungarian Compromise of 1867, which made the  Kingdom of Hungary a sovereign state, separated from the  Austrian Empire, with both states ruled by the same family.