Campaignmonitor seems to be "permission based", so you cannot send out Invites since invitees gave no permission. A current user deciding to invite another doesn't cut it as "permission".

If permission based is OK for your needs, AWeber is top of the line (www.aweber.com)

Here's a similar discussion: http://news.ycombinator.com/item?id=190633

CM focuses more on newsletter management, rather than automated emails like confirmations, invites, etc.

I second this. Crazy expensive for large lists, but it worked like a charm.