Now, you may ask why I find this small bit of the Bible of any interest at all. It is a good question. I believe in a single, unified God. I believe He is one single being. So, when I find Joseph, a child raised by a father who also believed in a single God but who is a prisoner in a city where the major religion worships hundreds of gods, being given a wife who is very likely the daughter of a Priest of a religion that teaches there is one, single God I find myself experiencing several emotions. Amazement comes to mind.
Had Joseph been presented with any other woman, he may not have accepted her because of the conflict in their religious beliefs. Or, he may have been drawn away from the God of his father to accept the gods of his wife. But here Joseph is presented with a woman who may very well been taught to recognize only one reigning God.
Of course you could say there is no evidence of Asehath's background. No, there isn't. But I find it a bit curious that we would even be told who this Egyptian woman's father was if there was not importance attached to it. When wives are mentioned in the Bible, their lineage is only important when something momentous is attached to it. Even men's lineage is subject to this peculiarity. For example, in Genesis 36:24 we find that one of the original peoples of Edom was a man called Zibeon who had two sons named Aiah and Anah. Anah is the one who discovered hot springs in the wilderness while he was grazing his father's donkeys.
Now, that single fact has no bearing on anything in the Bible that I know of. But for those repeating the oral history it would be very important for some reason. Perhaps the springs themselves became well known but this was Edom - the land of Esau, and not a place Jacob's descendants would bother with much. Obviously, only important information was added in the lineages of the Bible. You will find this kind of thing here and there where a recitation of names occurs.
Personally, I believe this particularly wife was probably selected for Joseph for the reasons I mentioned. God looked out for Joseph. The religious uprising in Egypt probably occurred before the children if Israel came to Egypt. Imagine for a second, a rogue Pharaoh suddenly breaking with hundreds of years of tradition to establish a monotheistic religion. A single priest of this religion has a daughter destined to become the wife of Joseph and a direct descendant of Jesus Christ. The god/man of Christianity. After the death of that Pharaoh, the religion of Egypt reverted back to polytheism and never again did such a thing occur.
Peculiar, interesting, amazing? I think so.