Blender Curve Manipulation Problem
If you find you are unable to move a curve handle in all three axis, it is probably due to the curve type being set to 2D. When you create the curve expand the Simple Curve dialog in the lower left of the viewport, or press F9: From here choose 3D and then, if you want curved splines, choose Auto in the Output Curve Type. The defaults are 2D and Vector and they may not be what you want for your curves....