Great question. Often, the debate is to what role the man plays in the home and what role the woman plays. I believe that the man and the woman share equal responsibilites. They should act as team mates. The main question to ask as to the woman's role is, 'What are her strengths?' My wife has certain strengths that I don't have, so she is more able to act in that role. For example, she is very good at teaching children. I teach adults. So, when it comes to our children's education, she tends to be more involved, with me taking a more supportive role.
We both are good at cleaning and organizing the house, so we both share equal tasks in that regard.
It is difficult to assess the woman's exact role without looking at each particular woman and recognizing the strengths she brings to the home.