Völsunga saga is not mythology as is usually understood. Sagas are in essence historical narratives, so it is no surprise that historical figures show up. A Scandinavian example of what you seek could perhaps be Saxo's "Deeds of the Danes" which is a history, but where Norse gods like Thor and Odin show up - although Saxo explains that they were not actually gods (Saxo was Christian) but wizards who used magic to deceive the people to believe they were gods. Another example would be the Illiad, which is also presented as historical but where gods play significant roles in the events.

King David is an example of such if you are not of the Jewish or Christian faith. He is mythologized within the Christian Bible. The most common example being the story of David slaying the giant Goliath.

The difficulty is that the line between myth and history is not particularly clear in pre-modern texts. Herodotus, for example, relates many mythological details, but he certainly takes himself to be writing history. Or take hagiography, hagiography abounds with legendary elements, but is about real people and often written by (or at least with the consultation of) eyewitnesses. I guess the answer to your question is thus a qualified "yeah, all the time."

A good example might be Alexander the Great, who we find mythologized in the Alexandrian Romances which were very popular in Late Antiquity and the Middle Ages. The story of Alexander's wall to hold back Gog and Magog even makes its way into the Qur'an. Many more examples abound.

I believe that Gilgamesh may count as an example of the kind of thing that you are looking for. Though the Epic of Gilgamesh was heavily fictionalized, it's generally agreed that Gilgamesh was as actual king of Uruk who reigned sometime around 2500 BCE. He is mentioned io several Sumerian documents and is listed in the King List. It is generally agreed that the historical Gilgamesh was probably was not a demigod however.