How to interpret the ban of unions between believers and non-believers? Having lately studied the bible from Second Epistle to the Corinthians I have pondered whether or not unions between nonbelievers and those in faith are really fully and undisputedly condemned by the scripture. There are numerous passages where they are at least discouraged if not bluntly denied as sin, but throughout the word there is the message of love, sharing and caring that seems to conflict this by limiting e.g. marriage to those who share faith. I'd like to hear your ideas especially regarding the passage on  2. Cor.6:14-16?

My question, hence, is: is the union (by union I suppose the reference is to marriage but I'm also interested if there is something to be said about cohabitation prior to marriage that is quite common these days) of a believer and a non-believer condemned without exemptions and in case of such marriage, is the one in faith committing continuous sin as long as the marriage lasts, and will that turn used against him/her in the final judgment?
Sex outside of marriage is strictly prohibited by the Bible. The Bible calls this fornication if you are not married or adultery if you are married but commit it with another person. 1 Corinthians 5 talks about this. It is for our own good that God prohibits this as this cleaves us unto the person that we commit this sin with.

The Bible also tells us not to associate with people like this as friends, as they might influence us. It doesn't tell us to ignore them or hate them, but to love them and pray for them. But do not invite them into your home as they might lead you or your family astray, and especially do not seek a lasting relationship with them (marriage) as this is being unequally yoked.


  Be ye not unequally yoked together with unbelievers: for what
  fellowship hath righteousness with unrighteousness? and what communion
  hath light with darkness?
  
  2 Corinthians 6:14


EDIT: I'll add a few references to not invite them into you home.


  I wrote to you in my epistle not to keep company with sexually immoral
  people. 10 Yet I certainly did not mean with the sexually immoral
  people of this world, or with the covetous, or extortioners, or
  idolaters, since then you would need to go out of the world. 11 But
  now I have written to you not to keep company with anyone named a
  brother, who is sexually immoral, or covetous, or an idolater, or a
  reviler, or a drunkard, or an extortioner—not even to eat with such a
  person.
  
  1 Corinthians 5:9


It is important to know that this speaks of so-called Christians that are living in open sin.


  But sexual immorality and all impurity or covetousness must not even
  be named among you, as is proper among saints. 4 Let there be no
  filthiness nor foolish talk nor crude joking, which are out of place,
  but instead let there be thanksgiving. 5 For you may be sure of this,
  that everyone who is sexually immoral or impure, or who is covetous
  (that is, an idolater), has no inheritance in the kingdom of Christ
  and God. 6 Let no one deceive you with empty words, for because of
  these things the wrath of God comes upon the sons of disobedience. 7
  Therefore do not become partners with them; 8 for at one time you were
  darkness, but now you are light in the Lord. Walk as children of light
  9 (for the fruit of light is found in all that is good and right and
  true), 10 and try to discern what is pleasing to the Lord. 11 Take no
  part in the unfruitful works of darkness, but instead expose them.
  
  Ephesians 5:3-11


The example of Lot's family living among the sinful cities of Sodom and Gomorrah should also be noted. Abraham decided to stay in the wilderness while Lot went for the much more attractive valley close to the cities. It was a disaster, as it ruined his home. His family was destroyed. Only He and his two daughters were saved, but it was too late. His daughters were already corrupted with the influence of Sodom and Gomorrah. Because of this, they committed this terrible and vile act of giving their father fermented wine and committing the terrible sin of fornication and incest.