OK... now that I am home I am trying to step through and it works for me. Just to be clear here are the steps I took...
1) Click on Multi-Player -> Internet
2) Click on the Host Game button.
3) Name and give all of the options (I tried with the Private Game both checked and unchecked).
NOTE: First possible problem is DLC. If you have DLC checked and the person you are trying to invite does not it might cause problems -- but you said you were not even able to click the Invite button.
4) Click Host Game button.
NOTE: I tried clicking the check boxes next to all of the player slots, but that did not prevent me from using the invite button.
5) Click on the Invite button bring up a list of friends who are online.
NOTE: One of my friends was online, and that was the only one listed. So make sure that you...
a) have friends
b) they are at least on line, if not in game.
Right now, since I was not able to stymie the game at any point, my guess is that your friend was not online and/or did not have all of the necessary game files (G&K expansion or DLC), and this might grey out the Invite button.
If you would like to test with me, I am currently online though no longer in game. Just request me as a friend and invite me to play after I accept and see if that works (I have G&K and all of the DLC). My username is the same as here... CGPanama.
