you posted in the InDesign user forum.
I think, your question is a InDesign SDK question.
So a moderator would best move this thread over to:
There is also a forum about:
Could you please help me on this ?
This is a known bug at the moment and is being investigated internally for a possible fix
When I wrote a drag from browser to InDesign, I had especially hard times with https URLs when the dragged image was wrapped into an <a href>. The culprit was something with Netscape in its name, e.g. kSysFileDataExchHandlerNetscapeHelperBoss is still around. Back then I used a bogus http link instead that I translated on the fly from the drop target (helper) side to perform the download on my own (curl). That code was last touched with CS5, though.