If someone used the phrase mixed marriage a generation ago they were probably taking about a white person marrying a black person. This is based on the concept of races, which is not in the Bible. In Genesis 1, it is very clear that God made each kind with the ability to reproduce after its kind. The modern science of genetics confirms this. There are genetic limits on different kinds cross-breeding. Nowhere does the Bible state God made different kinds of people. He created "mankind". God "made of one blood all nations of men for to dwell on all the face of the earth (Acts 17:26)." The life of the flesh is in the blood (Lev 17:11), and all people bleed red regardless of their skin tone or other minor varieties in their bodies. After the confusion of languages at the tower of Babel and the subsequent grouping of people into languages and nations (Gen 11), there have developed some cultural differences in various communities; but generally people are people everywhere you go and at all times. The wise king Solomon said, "The thing that hath been, it is that which shall be; and that which is done is that which shall be done: and there is no new thing under the sun (Ecc 1:9)." We all have a lot in common in our human experience. Since people of different skin tones can have healthy children together, this shows their physical compatibility. There are even instances of healthy twins being born looking like what some people call different races. When John saw the church in heaven, it is made up of "a great multitude, which no man could number, of all nations, and kindreds, and people, and tongues (Rev 7:9)." "There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus (Gal 3:28)." "Where there is neither Greek nor Jew, circumcision nor uncircumcision, Barbarian, Scythian, bond nor free: but Christ is all, and in all (Col 3:11)."
The important distinction the Bible makes between people is not physical. It is spiritual, especially in the New Testament. God does not care about our physical ancestry or even our spiritual ancestry (Deut 24:16, Eze 18, Jn 9:1-3). He cares about us individually and the state of our relationship with Him. "Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons: But in every nation he that feareth him, and worketh righteousness, is accepted with him (Acts 10:34-35). In God's economy there are only three spiritual categories of people: Jews, Christians, and Gentiles (1Cor 10:32), and the distinction for Jews is only based on God's faithfulness to the Old Testament covenant He made with them (Rom 9-11). So basically there are Christians and non-Christians. Non-Christians are called the world many times in the New Testament (Jn 14:27-30, Jn 15:18-19, Jn 16:33, Jn 17, Jn 18:36, Rom 12:2, 1Cor 1-2, Gal 1:4, Eph 2:2, Eph 6:12, Col 2:8, Jam 1:27, Jam 4:4, 2Pet 2:20, 1Jn 2:15-17, 1Jn 4:4-5, 1Jn 5:4-5 & 19, Rev 12:9). These scriptures make it very clear that there are only two cultures to God - the church and the world. They are directly in opposition in their values and actions, and will never be reconciled. We are either part of the church or part of the world. We must make all of our choices based on this reality including who we associate with. God does not require isolation for His people, but He does require separation in values and behavior. That is the very definition of holiness.
The most important personal human relationship besides that of parents and children is that of husband and wife. Children do not choose or have control over their parents, but people have control over who they marry unless they live in certain societies that are not free (in which case they would probably not be reading this anyway). The Bible is very clear about mixed marriages (Gen 6:1-13, Gen 24:2-9, Gen 26:34-35, Gen 27:46-28-9, Gen 34, Gen 38, Ex 23:28-33, Ex 34:11-16, Num 25, Num 33:55-56, Duet 7:1-6, Josh 23:11-33, Jud 2:1-3, and Jud 3:1-7, Jud 14-16, 1Ki 11, Ezra 9:12, Neh 10:30, Neh 13:23-27, 1Cor 6:14-7:1, 1Cor 7, 2Cor 6:14-7, and James 4:4-5).This is not mixing people of different skin tones or physical features, but of different values and lifestyles. Some people think they can find mutual ground or they can win their partner to their values. The Bible and experience show this is not what happens. The person with the higher values almost always compromises to the one with less. We need to understand that the choice we make in a spouse is possibly the second most important decision we will ever make next to obeying the gospel. We not only need to marry someone with the same beliefs generally, but someone we match with in more specific ways as well. This helps ensure we preserve our identity and pass it clearly to our children. Unity is essential in any endeavor. God made marriage the foundation of society. It is the first human relationship (Gen 1-2). Spiritual unity in marriage is essential, and is to be sought and guarded carefully.
The apostle Paul wrote about situations where one spouse refuses to be a Christian and the difficulties that arise because of that (1Cor 7). However, this is talking about someone who was already married when they became a Christian, or their spouse left the church. Life is challenging enough. We don't need to make it any harder by choosing to place ourselves in difficult situations that can be avoided with wisdom. When God is first, and we follow His word, He can bless our endeavors (Mt 6:33). When we place other things in higher importance than Him, we are setting ourselves up for failure.