In truth, there are no "Hispanics". Hispanic came from Hispania, then changed to mean people from Spain. Later, it was used in census to relate to any country that was under Spain's control. So basically, you have Latin, Spanish, and Mexican. Others form Europe can be referred to by their nationality. So no, I would not call a Mexican person Hispanic. They are from Mexico, not Spain (Spanish). Their ancestors where Mexican Indians...You can not group different races from different parts of the world into one "word for all". That's like calling Norwegian, Swedish, English, etc, all "white". They have completely different heritage, and different characteristics.
You also need to take in the fact of interracial relationships throughout the centuries. Such as when the Spanish conquistadors raped hundreds (if not thousands) of Mexican Indians. So over the course of time, you can have people living in Mexico with Spanish blood. Hence the "white looking" Mexicans.
Also, you can't deny that all races have some type of common physical trait. Whether it be hair, nose, skin... there are differences, which is what someone is going to use as a first guess (if they care). So no, you can't be a black/white "Hispanic". You can be of mixed races though, from any country (ever met a Black Irishman?).
When it comes down to it, why do you even care? My family is from Norway, three generations back. Though if anyone asks, I'm American.
Edit: Had to add something after Pana's post below. LMFAO. From "thanks to the white man" to your loose comment on dark skinned people you know being less well off than the light skinned ones. That is complete, racist, bs. I live in south Texas, and have dated mostly Mexican women (dark skinned, curly hair, and beautiful). Any one of them would tell you that the the "dark skinned" ones you are talking about need to get off their @ss and work harder, as none of them have trouble succeeding in life with hard work and clean living.
Lot's of people come from hardship, whether children of immigrants to kids raised in a trailer park. Though, out of all the people I have met in my life, Mexican people have been more racist than any other group. As well as the first to claim "racism" when something doesn't go like they wanted. Life can suck sometimes, no matter what color you are. Just got to suck it up, work harder, and stop making excuses. Cr@p, we have an African American president now. I would assume the majority of America (especially the younger generations) aren't as racist as you (and many others) would like to believe. I'd say the playing field is pretty well equal now.