I'm afraid I will be just shooting in the dark because I do not have and have never
used the AVR Studio.
Both the AVR studio and Arduino use the C compiler avr-gcc.
http://www.nongnu.org/avr-libc/user-manual/
But it Cautions there are caveats on using C++. See the avr-libc FAQ.
The arduino can handle class SDCARDclass which I use so that I can:
Preinstantiate SDCARD with line .cpp:234 SDCARDclass SDCARD;
This means that in the calling program I can just use:
SDCARD.readblock();
I dont have to in the program say:
SDCARD SF; //instantiate SDCARDFILES
then use:
SF.readblock();
My best guess is that your compiler version in AVR studio does not accept Preinstantiation.
In this case the .h and .cpp will have to be rewritten.
The class TVout is a good example of a class that does not use Preinstantiation:
http://arduino.cc/forum/index.php/topic,51867.0.html
Use that as a template to rewrite the SDCARD class.
If I had the AVR studio I would try it out for you.
But I'm very happy with just using the arduino IDE.