Do dual-supply switch ICs provide DC Offset internally?
You don't need to AC-couple your signal in or out of a dual-supply switch, and no DC-offset biasing is necessary - as long as your signal's voltage range falls within the switches' allowable range (determined by the supplies you give it).  

Your first circuit with a CD4066 has AC-coupling and DC-offset because it's not a dual-supply switch.
You need to shift your input signal up above ground for it to pass through the switch, and then AC-couple it on the output to get it back where it was.

VL is the Logic power supply. Tie it to whatever supply is used to drive the switches' control inputs. It doesn't have any effect on your signal through the switch.