The bar/bat mitzvah celebration, which is typically held either immediately after the ceremony or later that night, is not restricted by religious constraints, so you can involve all your relatives and family members in any way you see fit.
Whether or not the non-Jewish parent was restricted from participating in some rituals at the synagogue, the party is an opportunity to honor and thank that person.
A fairly recent tradition that is quite popular involves calling up relatives or friends to light the 13 candles on the bar mitzvah cake. This provides an opportunity to honor relatives or friends who were not honored at the ceremony, especially non-Jewish ones. (See Sample Candlelighting Ceremony Introduction and Sample Candlelighting Ceremony.)
Often bar/bat mitzvah parties are centered around themes. Your child’s theme could recognize the multiethnic heritage of his or her parents, through decorations, food choice, entertainment or party favors.
Many families also do bar/bat mitzvahs in Israel. Because Israel contains holy sites sacred to Judaism, Islam and Christianity, a bar/bat mitzvah in Israel could be a great opportunity for the family and guests to learn about different religious traditions.
The Bar/Bat Mitzvah Ideas and Primer for Interfaith Families is also available as a PDF document.