I have no clue what "white hispanic" is versus a "black hispanic" but oh well. I'm from Arkansas, we have white, hispanic, black, asian.
Hispanic generally refers to being decended from persons for whom Spanish is their primary language. (For a quick and dirty, and not well-thought out answer). So, in the simplest examples using visual inspection, if you look at someone and if you would have described them as "caucasion" but their sir name is Gonzales, they would be "white hispanic" or "caucasion, of hispanic descent" or etc...you get my drift. So if you have this pale skinned female patient whose name is April Gonzales, she's white hispanic. (I'm sorry, its an extreme example to just get the meaning across.)
Now the other extreme. You have a new patient, a Black Male. Says his name is, oh, what the heck, Tyrone Fernandez. Black Hispanic. Obviously. Oh, and yes you can have someone who is both Asian and Hispanic. This can be a convoluted, self-contradicting and touchy subject. I was a marketing consultant for a company that specialized in "target marketing" and we often targeted "racial demographics' so I really am familiar with how this is used and interpreted in the US at least. Not that there are not discrepancies, or those who disagree with the classifications, or with having classifications at all.
BTW, I doubt I'll ever actually meet someone named April Gonzales or Tyrone Fernandez, but hey, you never know. Those are just names I made up to use in an example. But I would classify myself as African-Amerian (or just Black American) and have dated women I would classify as Black Hispanic and as White Hispanic.