If I can be honest, I don't know in short. Though it was something that seems very practical and it really frustrated me I couldn't figure it out, there must be an add-on somewhere for it,
Though I think I may have come up with an alternative solution. If I can make some assumptions, it is important that you manipulate a curve not a mesh....You are not using it for a path and only for geometry... and you will be converting to a mesh at some point...
If this is the case, this file may have a solution that is not correct but may work, I have split the curve into two separate curves with two 'vector' aligned 'handle' at the points of overlap. Also manually added a curve to create the position required for a bevel.
So now all you have to do, is convert both curves to a mesh (You can join the curves if you prefer), Join the two objects together with Ctrl + J and then remove doubles, and now you will have a line of polygons at the exact point you want a bevel, just select them and raise appropriately.
(make sure you keep the vector aligned handles exactly overlapped, keep the resolutions exactly the same and do not edit the 'bevel curve' without altering both, I would delete the internal curve on one of the objects if you want to edit it's position, re-seperate it and then attach it exactly to the other curve object or add hooks/handles to edit both curves simultaneously (would you like me to do this for you?))
I hope this worked for what you intend to achieve, unfortunately unless I know the exact reason you want this feature I cannot give you a more suitable way to achieve it, this was just my best solution so far. I do want to investigate more, this does seem to useful.