The reason the line is changing in elevation up and down the curb possible is due to your line having geometry and the TIN being chorded. Depending on where your line is hitting compared to the vertices, it will elevate up the curb face or out into the paving.
Extract Surface Features which will allow you to extract a verity of information from a surface would be the best way I can think of.
3D Points and Lines from any surface
3D Lines from any surface
3D Surface Boundary from any surface
3D Breaklines from TBC Surfaces, for example subgrade surfaces
3D Drape Lines from TBC Surfaces, for example textured surfaces.
These are just a few of the things you can get from a surface with this command. For a complete explanation of the command, click the link.