Sewer line back up, cleanup my responsibility or cities?

I'm having trouble with my local water company. For the second time in a week their sewer line has clogged under the road . Both times sewer drainage backed up into my pipes and spilled out a vent pipe by my front steps. This isn't a small leak either it left a steady stream of sewage down my driveway and yard nearly 5 feet across of sewer water. Both times I have called the city and they unclogged their pipe. My question is whether it is their or my responsibility to clean my yard? It smells like an outhouse when I walk outside. Also the last time it backed up it blew up the top half including the cap of my venting pipe and rained sewer all over the top my front steps which is 36 inches off the ground. The pipe problem itself is down the street from my house.