"Inflate" polyline or shape into 3D with constrained edges?

I'm rather new to AutoCAD, and I've been trying in vain to convert some of my 2D Adobe Illustrator files into 3D.

The question I'm struggling with is how to "inflate" a polyline or other 2D shape into 3D with constrained edges around the perimiter. This image gives an example of what I'm trying to do:

Basically, pull/push an anchor point at the center of the polyline up in the Z direction, but keep the perimeter tied down on the XY plane. Think of blowing a soap bubble up through the polyline... 

Here's an example of what a colleage achieved in 3DSMax. I'm trying to recreate the three liquid drops indicated with the green arrows. The model shows liquid drops on a plastic (hydrophilic) surface.

Any ideas? I have a strong feeling I'm missing something very simple.

Thanks!