It is DISAPPOINTING that Skype now does not distinguish the different between Invisible Mode with the OFFLINE as Skype used to be.
I had enough with unsolicited calls and or stangers adding me while I am online, yet I now will miss lots of important calls mainly from family because they can not call me while I am on my Invisible Mode.
How sad and disappointed I am.
What version of Skype are you running?
I just ran some tests. I'm on version beta 5.7 and the contact I tested with was on 5.6. If either of us set our status to Invisible, we showed as Offline to the other, yet the other person was able to send IM's and make a video call to the Invisible contact sucessfully.
You should be able to get calls when you're set to Invisible. But maybe setting your privacy to "allow callers....from people on my Contacts list only" would prevent those unsolicited calls, even when you're online?
Please note: I do not respond to requests for help via Private Message.