There were a couple of awesome methods in Avenue for ArcView:
point=polyline.Along(percentage)
percentage=polyLine.pointPosition(point)
Don't laugh, but one of the reasons I updated to 10 from 9, was new method for Geometry
point=polyline.positionAlongLine (value,{use_percentage})
that is equivalent of 1st Avenue method (wrong name in my opinion anyway).
Does an equivalent of the 2nd Avenue method exist in ArcPy with ArcMap 10.2?