Firefox and Thunderbird has their own notification system, but if you want to use Ubuntu unified notifications here is tutorial how can you do that:

For Firefox download extension from here.

After installation, restart Firefox to activate the newly installed extension.

For Thunderbird:

Download the extension from here and save at your download folder. Open Thunderbird, click tools/Add Ons/ and drag and drop the downloaded extension to install it. Restart Thunderbird. Enjoy

Tags | Howto, Newbie Ubuntu Tips, Open Source, Ubuntu