In Jewish tradition, there is no verbal exchange of vows because the ketubah serves as a written statement of vows. When two witnesses sign the ketubah, the marriage is in effect.
However, in most Christian weddings, language involving promises of fidelity and loyalty is necessary for the wedding to be complete. The vows must be heard by at least two people for the marriage to take effect.
In interfaith weddings, there is often a combination of these traditions so that both parties to the wedding and their family and guests will understand this wedding as ritually complete and legal. Some interfaith weddings will have a ketubah signing, either before or during the wedding, and will have a recitation of vows as well. If there are two officiants, the rabbi or cantor will often preside over the ketubah signing and the minister or priest will handle the vows portion of the ceremony. In this way, families often feel a balance of ritual at the moment in the wedding that often matters most to them. The moment a couple commits to one another, publically, is the essence of a wedding.
With all wedding rituals with a single officiant or multiple officiants, these details are best discussed with the officiants well in advance of the ceremony to create the best fit for all parties involved. It is also important for a couple to give themselves ample time to think about the vows formula they would choose and time to draft their own vows should that be the direction they choose.
The Guide to Wedding Ceremonies for Interfaith Couples is also available in PDF and Word formats.