When you zero an item on the y axis it goes through the floor-grid because the zero value is in its center.
Is there a setting that makes the lowest part of the model being the zero value for the y axis?
Thats because the pivot point (rotation and scaling center) of the object is somewhere in the center of your object. So, simply move the pivot point to the desired "zero point". Look at this thread to see how that is done: http://www.daz3d.com/forums/discussion/29658/
But be careful. As said above the pivot point is also your center point for scaling and rotating.
Thanks, I thought that was the way to do it, but I tried in the past and it never worked right. Maybe I was doing it wrong I will look at that thread you linked and try again.