Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
If you mean by traditional marriage the one which is in conformity with the conditions of a marriage to be valid, like the inexistence of any marriage impediments, the presence of a Wali (wife’s guardian) and two (trustworthy) witnesses, but which is not officially registered in the court, this marriage is valid either with a woman of the people of the book, or with a Muslim woman.
However, if you mean by traditional marriage the agreement of the two parties to get married without the presence (or permission) of a Wali, so it is absolutely invalid either with a woman of the People of the Book or with a Muslimah.
In this regard, we would like to draw your attention to two important matters:
Firstly, a condition in getting married to a woman of the People of the Book, is that she should be following the religion of the People of the Book, either Christianity or Judaism, and that she should be a chaste woman.
Secondly, the priority is not to marry a woman of the People of the Book especially in present time because of the troubles that could occur in bringing up the children.
Allah knows best.