Comment 99 for bug 849416

So, there are at least three cases:
1. Invitation sent as a text/calendar message
   In this case you see the invitation as plain text.
2. Invitation sent as multipart/mixed
   In this case you see the invitation as an attachment.
3. Invitation sent as multipart/alternate
   In this case the invitation is ignored.

Also, try toggling mailnews.display.show_all_body_parts_menu in config editor and then using View - Message Body As - All Body Parts. (Caution! This will start marking all your multipart messages as having attachments. The marking will go away when you switch display option and reload the message.)