Very much against my desire, I went through separation and divorce 31 years ago.  I studied every verse in the bible I could find on the subject and became convinced that most people approach the subject with an attitude of, what will the Lord allow me to get away with, rather than what does the Lord want.
 
In the first few weeks I felt that the Lord was saying to me that if I stayed faithful in prayer then he would restore us as husband and wife.  I have never lost sight of that.
 
I also respect that other people come to different conclusions and have a number of friends who have re-married.
 
I came to see marriage as a covenant relationship between a man, a woman and God.  If one breaks the agreement and the other stands before God for the marriage then the covenant remains.  If both want the marriage to end and especially if they both express this through re-marriage then the covenant will not or should not be restored.  This is how I see the principals given in Deuteronomy chapter 24.  My own experience and the experience of many others confirms this to be a legitimate interpretation.  It is also in accord with the theme of the Old Testament book of Hosea.  The covenant also stands even when the "erring" partner re-marries (ofter for a short period).  I have heard of this happening in many cases, as well as my own situation.
 
When we were married I had no doubt that my wife was a Christian but in hindsight I am not so sure.  She grew up with a father whom I would term, a legalistic Christian and she still suffers from the effects of that upbringing.  Unfortunately in matters of Christianity, church going etc., she came to view me as a clone of her father.
 
I have not re-married and have held to the Lord for our marriage.  I was legally prevented from seeing my two sons for about 14 years, such was the depth of the relationship breakdown.  For the last 14 years we have become good friends and have been living in the same house but not as a married couple.  She remains antagonistic to religion or Christianity.
 
John Piper has an excellent  series on marriage.  He is the first preacher I have found in over thirty years who has taken the bible at face value.  I highly comment his series.
http://www.desiringgod.org/ResourceLibrary/Sermons/BySeries/78/
The last two in the series are very relevant to the above topic.
 
James

In my view, which I present in the book "Not Under Bondage", this is what the Bible says about divorce and remarriage:

* The Bible distinguishes between "treacherous divorce" and "disciplinary divorce".
* Disciplinary divorce is permitted by the Bible. This applies in cases of abuse, adultery or desertion, where a seriously mistreated spouse divorces a seriously offending spouse.
* Treacherous divorce is condemned by the Bible. It occurs when a spouse obtains divorce for reasons other than abuse, adultery or desertion.
* If the offending partner was sexually immoral, the Bible allows the non-offending partner to remarry.
* If the offending partner abused, deserted or unjustly dismissed the other, and the offender has been judged to be ‘as an unbeliever’, the Bible allows the mistreated partner to remarry .

Applying these principles to Steve's case, he is now a believer and has attempted to reconcile with his wife who professed to be a believing Christian. This was good and Biblically right on Steve's part. However, his wife has made it clear that she will not reconcile and they are now divorced.

Steve has approached his church leadership asking whether he has biblical permission to remarry. This is also good and correct on his part; he is not deciding for himself but seeking counsel and permission from his pastor/elders. This principle, that 'the parties concerned not be left to their own wills and discretion in their own case' is endorsed in the Westminster Confession. It is also endorsed by the Bible but from the information given I'm not sure Steve (or his pastor?) have fully understood the biblical principle of church discipline which should be used here to help answer Steve's question.

Matthew 18 would require that the church follow the four steps of discipline (vv. 15-17) to determine whether Steve's ex-wife should be treated 'as an unbeliever'.

If the decision is that Yes, she should be treated as an unbeliever, then 1 Corinthians 7:15 applies: Steve as a believer has been deserted by an unbeliever, so he is not under bondage.

Being not under bondage means he is free to marry someone else (so long as his new wife is a believer). This can be inferred because 1 Corinthians 7:10-11 applies to marriage between twp believers, who, should they separate, have only two choices: remain unmarried, or reconcile with each other.

Paul makes it clear that the marriages discussed in verse 15 involve a believer and an unbeliever, and the unbeliever being 'not under bondage' means he is not obliged to remain unmarried (in contrast to the believer in verse 11).

The Markan text is to be read in conjunction with Matthew 19, and should be seen as a case where Mark intentionally omitted some of the material which Matthew intentionally recorded. I argue that Mark omitted things which Matthew included because Mark was writing to a primarily Gentile readership but Matthew was writing for Jews.

In its turn, Matthew 19 is to be understood not as Jesus making an all-encompassing ruling about ALL divorce matters, but rather, as him carefully denouncing the presumptions and male-privileging distortions which both Shammaites and Hillelites were placing on Deuteronomy 24:1.

These are complex arguments and cannot be properly outlined in a brief comment like this. I suggest Steve reads my book to examine the arguments in detail.

I wish the arguments were not so complex, but I believe doctrine on divorce has for centuries suffered from multiple misunderstandings and false assumptions, which have so bedevilled the issue that it's no easy matter to untangle all the errors.

You can find my book by a simple google search. I won't put the URL here as that may be a contravention of Open House policy.