Marriage as a model of Christ and the church

In John Piper's book on marriage, This Momentary Marriage (Piper, John. This Momentary Marriage: a Parable of Permanence. Wheaton, IL: Crossway, 2009. Print.), he gives 3 reasons why one cannot say "that marriage is a model of Christ and the church" too often:
1) This lifts marriage out of the sordid sitcom images and gives it the magnificent meaning God meant it to have; 2) this gives marriage a solid basis in grace, since Christ obtained and sustains his bride by grace alone; and 3) this shows that the husband’s headship and the wife’s submission are crucial and crucified. That is, they are woven into the very meaning of marriage as a display of Christ and the church, but they are both defined by Christ’s self-denying work on the cross so that their pride and slavishness are canceled. (42-3)


Piper goes on to summarize this idea:
In other words, the main point in this chapter is that since Christ’s new covenant with his church is created by and sustained by blood-bought grace, therefore, human marriages are meant to showcase that new-covenant grace. And the way husbands and wives showcase it is by resting in the experience of God’s grace and bending it out from a vertical experience with God into a horizontal experience with their spouse. In other words, in marriage you live hour by hour in glad dependence on God’s forgiveness and justification and promised future grace, and you bend it out toward your spouse hour by hour—as an extension of God’s forgiveness and justification and promised help. (43)