I can reproduce this on two machines - basically I'm not able to invite anyone via iCal when I'm using Thunderbird for mail.
Here's what I've tried:
I configured Mail.app to use Thunderbird as the default mail client (Mail > Preferences > General > Default email reader (Thunderbird 126.96.36.199)
After that, I head into iCal, create the event, and add my attendee.
I've also tried checking my iCal settings, the most relevant one I see is unchecked:
iCal > Preferences > Advanced > Automatically retrieve invitations from Mail
...so will iCal only work 100% with mac Mail? I'd hate to have to tell our Thunderbird users to "downgrade"