How can we have a biblical marriage when, in today's culture, it's the government that grants us the right to a legal marriage that most churches accept as the only valid evidence of true marriage?
Furthermore, not all countries have the same marriage and divorce laws. So, whose country offers the most valid form of "biblical marriage"? In the Philippines, divorce is still not allowed, a Catholic relic. One Christian woman I know was abused and nearly choked to death by her worship-leader husband and had to flee. The court said too bad; you should have chosen a better husband -- a martial death sentence.
Years later, she fell in love and is now happily "married" while still not divorced. The modern church in the US would say she is living in sin, except that they are role models for how a biblical marriage should function. If she and her husband lived in the US, where divorce is allowed, they would be a morally accepted Christian couple. The only difference is a piece of government paper.
To answer your question, Paul, to me, biblical or Godly marriage has nothing to do with it being christened by a government authority. Bureaucracy didn't invent marriage. A Godly marriage does have everything to do with cherishing your spouse in the same way God loves and honors us and sticks with us through thick and thin. Also, we must mention there are millions of legally married Christians whose relationships dishonor God in every way. It's not about the paper.