Classifying the type of parents.?

I am doing a research on parenting. I would like as many opinions as possible. From your experiences, can you state the ‘type of parents’ you have comes across with some references to their behavior?

I’m not really a father yet so probably my idea won’t be good enough for you but still… I’ve heard that in a family, father mostly takes role as a “educator” sort, who will set up rules and teach the child many things about the world. While the mother shows her love and attentive, she would listen to her children’s story and problem so the children can live in harmony.
But that won’t apply in every family, since it depends on different types of parents relation. In general it seems there are 3 types of couples:

  1. The husband has the control and the wife is kinda submissive.
  2. The wife has the control and the husband is kinda submissive.
  3. Both husband and wife somehow have a mutual agreement and their roles are equal in the family (though I rarely see this situation).
    And so this husband - wife relation can affect a lot in parenting. For example, the couple (1) may have a father in main control, he can be manipulative and he likes everything under his control. Children have to listen to father, which can lead to various intense situations (or even abusive). Meanwhile the mother has less authority in the family, though she may not agree with her husband’s way of teaching, somehow she will be more attentive to her children. Thus the children can be much closer to their mother than their father.
    That said it doesn’t mean the couple (1) is absolutely bad, if the father, a.k.a the husband is a wise and knowledgeable man then there will mostly be no problem in parenting since he knows how to raise a child properly and treats his wife much better.
    The couple (2) also shares similar idea, except that the wife has the main control.
    Couple (3) seems to be the most ideal; however, it requires great understanding and knowledge about family life and how to treat family members properly.
    Besides knowledge and wise matter, there are other factors like money, and especially psychology but for now I can’t dig that in depth.