Initially, there was no qualification of marriage as secular or "Christian" - cp. Matthew 19:3-6. In a sense marriage transcends "Christian / Non Christian" distinctions in that all marriage is defined as a couple coming before God in order to express their vows in the form of a covenant witnessed by their Creator who responds to their covenant by united the two individuals into "one new flesh." Whether Christian or not, "what therefore God has joined together, let no man separate." (v. 6).
However, we are given principles in Scripture that limits a believer in whom they ought to marry: "Do not be bound together with unbelievers, for what partnership have righteousness and lawlessness, or what fellowship has light with darkness?" (2 Corinthians 6:14). Therefore, believers ought only to marry other believers. However, should something happen whereby a believer finds himself married to an unbeliever, they are not to abandon their vows and the covenant that God established that transcends the faith - but are rather to maintain faithfulness to the marriage covenant - 1 Corinthians 7:12-16.
Simply stated then, a Christian marriage is one wherein two born-again individuals have come before God reverently in order to be joined as man and wife and who thereafter continue to walk in a manner that honors Christ.