Whether you can use "Jig" or not, the essence of your issue is to help user to select a split point on a line/polyline (or in general, a Curve) with visual aid, which would show potential points to pick (not just anywhere along the curve), the length of the two split segments (as for the overlaps required as your picture show, it is just for extra calculation). That is, with a given line, you only need to visually guide user to pick a slit point. Once the split point is obtained, you can do whatever with it (actual splitting the line/curve into 2, extending the 2 segments to an overlapped range, ...).
Surely, you can create your own Jig to do this. Out of the 2 Jig classes - EntityJig and DrawJig - you would likely to use DrawJig for it. However, Since you want the single line/polyline entity being drawn as 2 separate entities, it would make things a bit complicated.
Since the nature of the operation is just to let user pick a point on the line/polyline, I think that it would be rather simple to call Editor.GetPoint() and wrap the call in between adding/removing a handler to Editor.PointMonitor(), and presenting visual aid inside the handler with Transient Graphics.
I took a bit of time to put together a small project showing the techniques of how to visually help user to pick a split point on a line. I'll post the entire code of the project in my blog shortly when I can find some time. Stay tuned.