I would like to put chair rail up a stairway, but the problem is that it would interfere with
The existing handrail. Which way is better - to put it above the handrail, below it, or even with it? I'm using half-round, so even with the handrail would make it tough to use the
Hand rail. Also, what height? I would like to tie it into my existing chair rail around the room that meets up with the hallway, but at 30 inches, it looks ridiculously low up the
Stairway (the ceiling is about 16 feet at the foot of the stairs.

Remove the railing and when your done re-install the rail to where you think it looks better. More than likely above the chair rail from 32-36" off the stair nosing.

For the chair rail you can measure off the stringer 30" also. You'll have to install a vertical piece of chair rail from the hallway chair rail to meet the chair rail going up along the stairs.

Of course these will all be mitered. Your angle of the stringer will be any where from 34 to 38 degrees.

Hope this helps. If we were able to draw here it would be easier to show what I mean.:)

Why do you need chair rail up the stairs. I do believe that a handrail would look much better (by itself) and would be more practical. Otherwise, there is too much going on.