Hi,
What a coincidence that you've replied cause I was currently testing what MS suggest me.
There are some options in IIS to configure the Failover behavior with either HTTPLevel and TCPLevel. By default, it is configured to use the HTTPLevel. I've tried to set it to TCPLevel on my side without any luck. Maybe it'll work for you.
She also told me that there's supposed to be a setting in the load balancer to be "HTTP aware" which should solve our issue.
Also, I just saw that I never mentioned that we currently have a workaround for that issue. It is working but it's not good enough for us on our side.
We have copied html pages at the root of each sites containing a single line of text (ex: LOAD BALANCING PAGE). We then configured new monitors on the load balancer to "SEND STRING : GET /htmlfilelocation/htmlpage.html" and "RECEIVE STRING: LOAD BALANCING PAGE". This way, when the site is stopped, the load balancer is unable to read the html page.
Maybe that could be enough for you. On my side, I've contacted our Load Balancing team to see if they can find that "HTTP Aware" option on our LB.
I'll get back to you when I have more details.