If I understand what you are trying to do correctly...
First, make sure PLANAR is active in the status bar at the bottom (the box appears light when activated). Also, have the Osnap control box open (the one with the little checkboxes - click in the Osnap pane in the status bar if it is not showing).
Then, start your curve, and snap to the first point. Then, before you snap to the next, check "project" in the Osnap box, then go and finish your curve. The curve should all be on the plane parallel through the first snap point (that's what Planar does) but go through the snap points projected to that plane as well.
The thing to understand is that without Project on, Osnaps take precedence over Planar, and the snap will go to the real snap point, not the projected one. And that if you have Project checked for the first point, the snap will be projected to the current CPlane. Project with Planar OFF will project everything to the CPlane.