eh... I don't understand either, and I'm christian.

You say you are the head of the house, but you seem to practice mutual submission, or see your wife as equal. Could you please explain what the concrete difference is between you and your wife, in this department?

Because you said
and I don't see where the (wifely) submission (or male headship) comes in.
That's because you are analysing marriage based on cultural definitions of submission and headship instead of Godly ones. What I am trying to say is that we define submission and headship differently than those things have been portrayed and exercised throughout human history. "Head" does not mean "boss" in God's design, and "submit" does not mean "obey".
I have given the the definition of
hupotasso before. There is nothing in the non-military definition that grants authority in the relationship or creates a hierarchy. In fact, the same word is used for Christians in our relationship to one another. None of us have authority over any other, and none of us are higher in rank than any other. We all are to "display a voluntary attitude of giving in, cooperation, assuming responsibility and carrying a burden" with each other. No one is higher or better than another.
The "headship" role is one of resonsibility, not authority. We are to model Christ, who was a servant leader, not an authoritarian leader. Jesus modeled what our responsibilities are by serving the church, interceding for her both in the world and with the Father, and being accountable before God (even onto death). In a nutshell, Jesus succeeded in all of the responsibilities Adam failed in. Jesus, even now, is in heaven serving and interceeding on our behalf.
NONE of this has anything to do making family decisions or outlining specific roles and duties between the spouses. Such heirarchy and role distribution NEVER occurs in the biblical teaching about marriage (although it certainly occurs in biblical history, a very different thing and opposite thing from biblical teaching). Adam and Eve were eqaul partners in the garden until the fall. When that happened, the curse spells out how men and women would behave towards one another. But the curse is not God's design, it is our inclination because of sin. Even still, we can strive to work toawrd the Godly design instead of the cursed wordly design. The entire record of biblical teaching on marriage all points us in the direction back to God's original design of equality.