Fiction; Female Protagonist, Adopted, Middle East, Circassian, California, Doctor

Trying to find a book that I read in the 1990's/early 2000's. I can't remember the title or the author. I believe the author is female. I think this was written around the same time as Princess: A True Story of Life Behind the Veil in Saudi Arabia by Jean Sasson (1992). It could be later than that though. Although the book has Circassian characters, it is NOT about the Circassian people.

Cover:
I think it had a picture of a desert below and woman with her head and bottom part of her face covered. The color of the headscarf was black. I don't know if the book is still in print and maybe the cover has changed.

About the book:
Fiction
Adventure/Romantic (not a "Romance" book per se)
Main Characte: Female; name Liz/Elizabeth, doctor, doesn't know she's adopted, lives in California, meets a Middle Eastern man and has a romance with him; he brings up that she looks Circassian and that's what makes her wonder if she is adopted; tries to find out more about her birth mother
Adoptive parents: father is in US military, present in the Middle East during a conflict; mother is housewife
Biological Mother: Circassian born, red hair, fair, green eyes, very young; wife to Arab man; lives in Middle East; gave up baby to adoptive parents at a US Military vessel while it was in Middle East