Matt. 18:15-17 "Now if your brother sins against you, be going, and show him his fault between you and him alone, if he hears you, you gained your brother. But if he does not hear,take along with you yet one or two, so that 'by mouth of two or three witnesses every word shall be established.' But if he refuses to listen to them, tell to the assembly; but if he also refuses to listen to the assembly, he shall be to you just like the heathen and the tax collector."
Who are the proper candidates for the action spoken of in these verses?
"Now if your brother sins against you..."
A 'brother' would be anyone who is part of the assembly which profess the faith of Christ, therefore making the parties in this action fellow christians.
"...be going, and show him his fault between you and him alone..."
Here Jesus does not elaborate on any particular sin or sins. Therefore we may not speculate or vainly imagine sins which do and sins which do not fall under this general and plain statement of Jesus. Yet,we may meditate upon the wisdom of the proverbs here where we read, "Hatred stirreth up strifes: but love covereth all sins" and "The wisdom of a man hath deferred his anger, And his glory is to pass over transgression" (Prov. 10:12, 19:11). And again we read, "Brothers , if anyone among you is led astray from the truth, and someone turns him back, let him be knowing that the one having turned back a sinner from the error of his way will save a soul from death and will cover a multitude of sins." (James 5:19,20) Note James address is to 'brothers' and 'anyone among you'.
The first step being done, and to no avail, leads to the next step where the offended party is to "...take along with you yet one or two..."
After these two more informal proceedings have failed to bring the offender to remorse and repentance,the third and more formal step must be implemented and they must, "...tell to the assembly...".
If after this third step with all of the above being done in the spirit of Ga. 6:1 "Brethren, if a man also may be overtaken in any trespass, ye who are spiritual restore such a one in a spirit of meekness, considering thyself--lest thou also may be tempted", "...if he also refuses to listen to the assembly, he shall be to you just like the heathen and the tax collector."
The Word of God states it plainly that there may be no other recourse than that which has been clearly delineated in the Words of our LORD Himself.
To answer your question, "Is a wife of a believing husband also his sister in Christ?", The simple answer is yes.
To answer your more difficult question, "Would this apply to a married couple as it would to any other brother or sister in Christ?", the framing of your very quesstion is a good indicator that there's more which would need to be said than that which has been said above. A married couple, (as has been mentioned already by another on this thread), have a different relationship as well as different responsibilities and duties to one another, and they're not merely 'any other brother or sister in Christ'.
Much else must be taken into consideration before,during,and after these steps are proceeded upon. Each particular case may vary, yet we are never to neglect the Word Of God to follow our own course of action thinking we know better.
It may be that marriages could be saved by following Christ's clear directives even in marital relationships. And why not if we truly trust in the Living God, His Word and His Power.
As one has rightly stated, ""Strangely, some never think of using church discipline, even informal discipline, when the two parties are husband and wife. Why not? A Christian husband and wife are not merely married persons, they are also brother and sister in Christ's church. Most marital problems could be resolved early by active, informal disciplinary action."
If the objection be made that this may open wide a door for a rebellious wife to exaggerate her husbands failures and expose some of his sins (or a prideful husband may do the same), I very well concur that this may indeed follow. Yet, we cannot ignore nor neglect God's express command to us as to how to handle offenses. The mere possibility and probability of this occuring must give way to our faith in an omniscient God rather than in our own wisdom and/or lack of it. Sin will surely show its ugly head in these and other matters, but may we be ever so discerning and be wise as serpents and harmless as doves.
My concluding thought is that if your husband or wife "...shall be to you just like the heathen and the tax collector", how might this look in practice in comparison to your relationship 'to any other brother or sister in Christ'.
I know that there are some who'd take this to very unbiblical forms of action. I have seen the positive and the negative of all I have discussed above.
Sin plagues us all, that is one reason why Jesus said, "Beware of men" (Matthew 10:17).
Beware of men - "prosechete apo ton anthropon" in
Greek - hold your mind away from men. Be on guard
against men. Beware of men.
The word "men" is the English translation of "anthropon." It means "human beings" (Strong's #444). Our English word anthropology comes from this Greek word "anthropos." Anthropology is the study of mankind. And "anthropon" refers to human beings in general. Jesus said,
"Beware, be on guard against, human beings."