Real web designers - those who can do both the design and then the coding with HTML/CSS, or who can produce a design directly in HTML/CSS are a rare and very valuable thing.
Wether they're appreciated on the market - I don't know, but they should and hopefully they will.
Besides if you CAN do both and work as a freelancer you could potentially do insane amounts of money.
In the end it boils down to what you want to study.
xterm wroteGo for Graphic Design if you're already artistic, augment your skills with "Learning to program" later on (or during).
The inverse is NOT possible.
From what I've seen with the graphic designers I work with, this is hardly possible... They seem to have a very hacky/patchy approach to programming (copy paste code from around everywhere). Maybe they use the same approach they use for graphic design which is research, copy a little from here and there and what matters is the result... it doesn't work for programming. Also, years of working with Photoshop/Illustrator where you can build a blueprint in 1/2 hour (and get paid good money for it) doesn't exactly prepare then for the painful process of coding.
But seriously, do you believe that it's NOT possible? Everything is possible, just harder.
Why learn one and then the other anyway, why not learn in parallel? That would make a real website creator.
I looked at various programs, however, and so far the AUB program seems best.
AUB has a good graphic design offering anyway (so does ALBA, incidentally). But they won't prepare you to program, and probably won't give you any time nor appreciate you learning it in parallel. For real parallel majors, look outside (Paris, or other places, where some school offer "media" or "multimedia" (or whatever it's called) degrees)