There's nothing in the Bible that would prohibit interracial marriage.

Keep in mind that there's really only one race, the human race; we all have a common ancestry; we all come from the same genetic material.¹  Due to this, everything one is, the other is also.  If you dislike another due to the color of their skin, then, in all actuality, you dislike yourself.

Bible References:

¹ (Genesis 2)