Recently an emailer asked what God would not consider a scriptural marriage. Most teach that the only invalid marriage is to a non-Christian. When one of their children then marry someone who is not a believer or does not believe as they do they usually reluctantly accept the union as a marriage.
The scripture actually says quite a bit more about "marriages" that God would not consider valid, but most of this would be very politically incorrect and also the opposite of what mainline Christianity teaches today.
One example is that we are not to marry children of incest. The children of Moab and Ammon are probably the best well known, but the children of Canaan are also children of incest. Most do not understand that in Genesis 9:22 Ham took advantage of Noah's wife while Noah, and probably his wife, were drunk with wine. Canaan was the result of that incident. That is why Noah rightly cursed Canaan.
I remember looking at the definition for adultery in one dictionary. It said, "to commit adultery" and then something about "marital infidelity". Not very helpful. What does help is to know the source for the word adultery. Adulteration means to mix. The seventh commandment is not just about marital adulteration which is a mixing of seed in a married woman. There are statutes in the scripture that explain each commandment. Adulteration is forbidden for farm seed, animals and cloth. These are all health regulations at the very least. Hybridized plants are plants that God did not create and may lack nutrition. Even clothing that is made of man made materials may not absorb sweat and that is a health issue.
Mixing of different peoples also has implications that most ignore. One could check with medical knowledge, anthropology and history for some clues as to why. Better yet one might read the seventh commandment as, "Thou shall not adulterate". The Septuagint is a bit more direct in the Greek in that is says, "Thou shall not mongrelize". That one is pretty tough for most people to hear these days, but God said it. It is what God actually said in his word and if you dig a bit deeper you will see that adulteration has that same meaning.
For the benefit of your own study consider the word bastard in the KJV. Today's definition has to do with a child born out of wedlock. Here is the scriptural definition from Strong's and Brown-Driver-Briggs combined. By the way, there are verses in the new testament that show that this commandment continues and at some point I may add those, but regardless you now know the original intent of "Thou shall not commit adultery" which is still found in Romans 13.
alien (or to alienate), mongrel, child of incest, mixed population. born of an Israelite and a non-Israelite.
Other than that I would recommend looking at the list of scriptures here. After that it is more a matter of what one is willing to allow God to show them. A person who has already made up their mind will not see new information in the scripture.