Is there anything unique to a christian marriage that non-christian marriages are deprived of? Are there any teachings that state that there is anything unique to a Christian marriage that non-Christian marriages are deprived of? 

A slightly different question but similar enough:

Does a couple that "goes to city hall" and enters into (what they believe to be) a strictly legal agreement of marriage also unwittingly enter into the same holy covenant that Christian spouses have?

Along these lines, from the question: What is the moral status of common-law marriage?, Caleb states:


  Christianity even honors marriage as sacred when entered into by two
  non Christians with a purely secular profession. God's role in the
  covenant relationship is something we believe just is -- even if the
  parties involved ignore him.


(Could someone provide scriptural references for this assertion?)

Assuming what Caleb states is true, I understand the idea that a Christian marriage will have the privilege and benefits of working with God instead of against or in indifference to Him, as in a secular marriage. My question is not about the effect of the "quantity" of God in a marriage - rather, is there any special qualitative distinction between the two marriages? For example, the Holy Spirit dwells in a Christian, but not a non-Christian - is there anything analogous to this for the two kinds of marriage?

I'm mostly interested in this from a protestant perspective. It goes without saying, but in order to minimize opinion and open discussion, please derive any answers from scriptural references.
It may be helpful to do a little set up first. There is a difference between indicative and imperative statements. An indicative is a statement of fact; there is no ought in it. The chair is brown; the ship is tilting, etc. An imperative is a command; it tells what we must do. Close the door; turn off the tv, and so on. Paul says, "'Therefore a man shall leave his father and mother and hold fast to his wife, and the two shall become one flesh.' This mystery is profound, and I am saying that it refers to Christ and the church. (Eph 5:31-32)" He's not saying that this is the way it ought to be, but that this is what marriage is, what it means fundamentally. As he goes on, he fleshes out the picture with instruction (imperatives) for husbands to love their wives and for wives to submit to their husbands. 

Every marriage is a picture of Christ and his bride, the church. The scripture makes no distinction between good and bad marriages in this regard, whether heathen couples or believers. All marriages proclaim to the world how Christ relates to his church. Because of sin and rebellion, many of these pictures are slanderous lies concerning Christ. But a husband can never stop talking about Christ and the church by how he acts. If he is obedient to God, he is preaching the truth; if he does not love his wife, he is speaking apostasy and lies – but he is always talking.

In another sense, a "generational " or "covenantal" sense, there is a difference. Paul says, "If any woman has a husband who is an unbeliever, and he consents to live with her, she should not divorce him. For the unbelieving husband is made holy because of his wife, and the unbelieving wife is made holy because of her husband. Otherwise your children would be unclean, but as it is, they are holy. (1 Cor 7:13-14)" So in this sense, an unbelieving couple would be outside the covenant body of Christ, while a couple with even one believer sanctifies, or covers the children and they are counted as covenantal members. This is not to say that they are 'saved' but that they are connected to the body covenantally.