Several neighbors have also had the same problems. Our sewer company Metropolitan Sewer District, MSD, hired a plumbing contractor in 2013 and installed a back-flow prevent valve. This was supposed to fix all our problems.
It didn't work and several neighbors failed also.
So now the latest fix is MSD hired a contractor to install a tank, pump, etc. this has supposedly disconnected us from a gravity sewer system and now our sewage is pumped into the main.
I wonder if this fix will work. Time will tell.
Update:
It didn't take long for this new system to be tested. We had 4" - 5" of rain on August 15. Several neighbors had sewage in their basements. Our basement stayed dry. So I guess the new system has worked. We feel sorry for the neighbors.