Only problem I see with it is the different backgrounds coming into the relationship. Make sure each understands the background. How is the family on both sides going to react? is both people ok with that. Some may react badly but if both are ok with dealing with that and avoiding the person that reacts badly no problem still. How is the area for that and how will that affect kids. If your willing to move later when you have kids to a more supporting area that's still not a problem. What are your beliefs and values are they the same? crazy as it may seem these cause more problems than any other including race. it's the root behind the " i think our kids should .... " then "I don't think our kids should ...." It's mainly because of different values.
Truth is if your in love not lust, you understand the problems ahead, your willing to deal with the problems ahead then there is no problem. If your not willing to deal with the problems ahead then you'll find problems arise and that can sometimes be more complex if the 2 is from different races. If your willing to deal with the problems ahead no matter how complex, there will be a good relationship.
race isn't an issue in the bible, it's culture. it's important to understand that race can complex the situation, but if you can both commit to the relationship, it won't matter.
shortly after civil wars times white and black couples made it and in culture things don't get any tougher than that. so it's not foolish to think interratial relationships can make it today.