Yes! You can read all three parts of The Search and The Promise online. Both parts of The Rift can be found online as well.
An additional comic book that was published, Avatar: The Lost Adventures (it features never-before-seen adventures of the gang), can be viewed online also!
NOTE: Be sure to read The Promise first because it leads into The Search! And The Search leads into The Rift!
The Promise → The Search → The Rift
Read all parts of The Promise here.
Read The Search: Part 1 here.
Read The Search: Part 2 here.
Read The Search: Part 3 here.
Read The Rift: Part 1 here.
NEW: Read/Download The Rift: Part 2 here. (Thanks to norsepearl for the link!)
Read Avatar: The Lost Adventures here.
ALSO NOTE: The Rift (Part 3) will hit comic book stores in November 2014.
All of them are definitely worth the read!