Having extensive search on the net, I just figured out that the AFC2 support has to be explicitly enabled on iPhone before you can browse the directory "Raw File System" on iFunbox. There is no other way at the moment to turn it on except jailbreak your iPhone.
I am very Sorry!
Here is the quote from the net:
"The com.apple.afc service runs on the iPhone and is what iTunes uses to sync media to the iPhone.
This service is restricted to providing file system access to the Media folder. The service is "in jail".
The original meaning of jailbreak was to modify the service so that full file system access was possible. Later it was realized that a second service, com.apple.afc2, could be created to give full file system access to third party tools, while leaving com.apple.afc for iTunes to use.
iPhoneBrowser, other manzana-based programs, iBrickr, iFuntastic and iNdependance use the afc2 service to access the file system and allow the transfer of files such as Summerboard themes, NES ROMs or eBooks to the iPhone. "
However, if you can manage to see the /var/mobile/Library folder but not the file notes.db, please do expicitly create a note on your iPhone before giving up too early, because feedbacks from some of the users that they would be able to see the folder and the file only after they create one.