"Overall headship of family belongs to men"?!
DIVISION OF LABOUR ––
A man and a woman are physically different from each other, by birth. The wife who gives birth to children is mainly responsible for their upbringing and this takes much of her time. Thus to earn the living Becomes the responsibility of the husband
Thus the difference in the responsibilities of a man and a woman arises out o their physical and biological difference. It by no means follows that man is superior to woman.
[Islamic Way Of Living by Syed Abdul Wadud]
The Quran in the context of family life:
2:228 ---- Women, in all equity, have rights similar to men --.
2:187 ---- They are your garments and you are their garments close to each other, source of mutual comfort, complementing each other, trustworthy and keepers of privacy, reason for décor, and re-dressers of faults.---
So, No! There is no head but only two EQUAL partners, wife and husband.