Jewish theology has nothing to do with Christian theology, since Christ is totally out of the picture. So why bring it up?
Because the first post asked..."How do Jews interpret, what Christians interpret as Genesis 3:16? "
That was my answer. Jews will probably interpret it the same as Christians.
However, there is a lot to understand about ancient Jewish rabbinical forms of interpretation of the Old Testament that can explain why their people were so dull to understand anything at the time of Christ.
They had taken the key of knowledge (the scriptures properly interpreted) and had added so much to it as to render is incomprehensible and unlivable.
Luke 11:52 Woe unto you, lawyers! for ye have taken away the key of knowledge: ye entered not in yourselves, and them that were entering in ye hindered
But except for those that might have invented allegories and elaborate interpretations by counting the letters of the sentences in Gen 3:16 they probably would have interpreted it the same as Christians. That being said not many Christians seem to interpret it well using it as a source for why a woman should submit to a man rather than referencing it as consequences of the fall. Both Christians and Jews, and muslims use it to say that it teaches that God's plan was for women to be ruled by men. And that's a bad interpretation.
Teaching about the order of the family and marriage does not require using this text in a way that does not observe the negative nature of the man ruling over her was a result of the fall. That should be noticed when people read this and not ignored.