If you are going to use Holy Scripture as a reference, there are a lot of passages which can pertain to this issue. Many times we think we can marry someone and then we can change them or they will convert to our faith - but we should not expect this because it is not true at all. God does not make this promise. Instead we should walk into it knowing we cannot change another person, that there is no guarantee that they will become the same faith, even if they tell you they will - it has to be a heart conversion, a gift/grace from God, not an agreement born of romantic passion, which may not last.
Only what's built on Christ will last...I believe non-Christian marriages can make it but they lack the fundamental grace of the union as God instituted it by not basing it on spiritual principles, and only on human love for each other, which so easily can fail and is rife with imperfection, which is why we look to God for guidance and strength to be able to truly love another, in good times and in bad.
Many times a partner who does not share your religious viewpoint can slowly tear your faith apart by constant planting of seeds of doubt and then there is the question of how to raise the children.
Marriage is the union of body AND soul, as Scripture puts it, can two walk together unless they are agreed? (Amos 3:3)
I don't know if this what you are asking, and I wouldn't use Scripture for a non-Christian, but I believe your profile states that is your Faith persuasion. :) Atheists and non-Christians need not start an argument, I was referring to the Christian belief system only and in no way am implying non-Christians can't have beautiful successful marriages.