I think I can see what you are getting at. The power supply for your inverter cannot share any common reference with the load - if you want to make one side of your load grounded, then the power supply must be floating with respect to ground. That way, you can connect one output of your full bridge to ground (call that "neutral") and the other will be "live".
If you measure the power supplies of the inverter with respect to ground, you will see ripple equal to half the output voltage swing superimposed on the DC rail voltage.
I hope this makes sense - I don't have the facility to draw a picture at the moment, otherwise I would do a diagram to explain it better.