Is the term "within" the veil used to indicate being African American and "without" being white?
Since the veil indicates a mask between African Americans & whites, the terms within & without are a bit confusing.
You are right to point out that the veil is a mask between African Americans and white Americans. However, it is quite clear that DuBois is using "within" to refer to African Americans and is saying that the white Americans are outside the veil.
To see that this is the case, simply look at the first time that the veil is mentioned in the book. There, DuBois says
Leaving, then, the white world, I have stepped within the Veil, raising it that you may view faintly its deeper recesses...
From this, it is clear that when one is inside the veil one has left the white world. What is inside the veil is the black world. In this book, DuBois is trying to impart of white Americans what it is like to be black in the United States. He is trying to take them inside the veil so they can properly understand black people.