JFBC-invite email pop up window hiding behind other published modules.

Try looking at the post below which is from a user with the same issue. It's the best explanation I can give:
www.sourcecoast.com/forums/topic?id=1713&p=1#p7274

If you still run into issues, please send us a link to the page that you have the Invite module published on. While our solution (above) works on about 90% of sites, there are a few it doesn't work on, so just let us know and we'll see what we can do.

The problem is caused by Facebook not letting us resize that frame. All we can do is widen our module's div so that it stretches whenever Facebook tries to display something outside of the default width (like the Send Invitations) dialog window.

Our Javascript is actually firing correctly and widening our module. The issue seems to be that your template itself has a few CSS settings that are preventing the widened module from being displayed. If you're up to it, please try the below changes and see if they improve the situation. There will still likely be some minor issues, and you'll need to make sure it doesn't cause problems with other features of your site, but hopefully will put you on the right track:
Both of these changes are in the /templates/getreserved/css/template.css file
~line 1852, in the "s5_modulemm-whiteblue" declaration, change:
overflow:hidden; to overlow: visible;

~line 1031, in the "s5_mainbodybread" declaration, make the same change (hidden to visible)

Let us know how this goes. We can only test so much on a temporary basis, but that seems to make things better..

Best of luck, and let us know your results!

Fatabjobe,
There's 2 more styles you can try to add, but I'm not sure if they'll fix your problem. I also can't see the module on your page anymore to test these changes, but I can understand if you disabled it temporarily.
In the "s5_modulemm-whiteblue" declaration (~line 1852), add:
z-index: 100;
background: #FFFFFF;

Hopefully, this will give the invite module a background color of white, and when it's widened, make it on top of anything else.

Unfortunately, if this doesn't work, the next best suggestion I'd have is to make it so that Invite module can't overlap into another Facebook widget. They both use iFrames to display their content, and iFrames overlapping can cause some of the issues in your picture above.

Hopefully one of these solutions will help, and not be too inconvenient. Good luck!