Can Route Hatch Symbology be converted to points?

I have a request to help someone out that wants to cut some road lines into 0.1 mile segments (more than practical using a manual method). I can easily portray the 0.1 mile locations using the Hatch tab on the layer properties for the routed dataset in Arcmap. What I don't see is a what to "export" those point locations as a point dataset which I could then cut the lines with.

Is there a way??

I don't want to densify the lines & then split at vertices because the 0.1 mile interval is too great and I'll end up with too many unwanted line segments that I would have to clean up.

Thanks!
Steve