First off, I'm not Greek -- I'm of northern Euro extraction (various cultural groups). So if you're only looking for the Greek opinion, ignore the rest of what I have to say.
Colourwise, I'm what you'd call white: definitely melanin-impaired. I rarely tan, only burn. My skin tone in summer ranges from pale white to burnt red to pink back to white. I'm like an extremely slow-blinking neon light.
That being said, you'll get varied answers on who is "white" depending on who you ask. A white supremacist will limit it to northern Europeans (Germanics, Celts, and maybe western Slavs only; Balkans, Mediterraneans, etc need not apply). Ask a black man who's white, and he may say anyone who isn't black African or east Asian -- some black people include south Asians. An American police officer distinguishes a "hispanic" from a "white", while a person of Aztec ancestry certainly would not. A former co-worker of mine is white-skinned as I am: but because he is of part Miqmaq ancestry, he's considered by many to be an Indian. (First Nations)
Thus, "White" is not really a true cultural or ethnic reference -- it's a very vague term with political overtones.
Your mom may be white, but she has a culture and ethnicity, as does your father. Your ethnicity is a mix of your father's and your mom's. If your mom is French, then you're half-French and half-Greek. If you are a citizen of Athens, you are a half-French Greek citizen, or a Greek of part-French extraction.
Your culture has to do with where you're raised, and by whom.
As for me: my ethnicity is Anglo-Saxon English on my father's side, and English/Irish/Scottish/Norman on my mom's. My culture is Newfoundland: an Anglo-Irish derivative. My nationality is first-generation Canadian (my parents were British subjects until 1949). My colour is white, no getting around that. But if my cultural/ethnic ancestry were anything other than it is, SOME people would consider me white, others no.
BTW, my personal definition of "white" is "European Caucasian" - so it includes Greeks.
Does this help any, or does it muddy the waters?
All I'm saying is just be careful using politically-loaded terms like "white", especially when you are using it to distinguish from a specific ethnicity/culture, like "Greek".