My policy says Liability, and that's exactly what the fuck it is. Break it down further to bodily injury and property damage all you want, it's still liability. Dumb ass.
You can ALSO have liability on your homeowners insurance, but that's generally an umbrella policy that covers pretty much any kind of liability and has nothing to do with cars.
My umbrella covers auto liability beyond the limits of my regular policy. The policy actually sets minimum limits I need to carry for home and auto and it covers up to $1m beyond those. Costs like $250/year. Way cheaper than upping the limits on all of your other policies to cover a major loss.