The screen shot is consistent with what Dan pointed out, you cannot use Union when one of the event tables is a point event table. Notice that the output event type setting is Line and that setting cannot be edited to change it to Point. You can only create points when a point event table or feature class is used with any of the Intersect tools and points simply don't work with any of the Union tools.
The workaround is to create two new fields to hold duplicates of the real measure fields of your line events. You should use the duplicate line measure fields for the inputs to the tool. Do an Intersect with the points, not a Union. Make sure the output measure field name is not the same as the original measure field names used by the line events. The output will have a new measure field for the sign point location created by the tool, but it will also have the original measure fields.for the line. Just use the two measure fields preserved from the line that were not inputs to the tool to create a line event layer. The layer will contain line events with the original line data combined with the data of one of the signs it touched, and there will be overlapping lines that will match the full set of signs touched by each segment.
In case what you really want is a single line event that has many columns of fields that combine the data for each and every sign along the segment into a single event, no tool does that. A Pivot table could pivot one of the sign attributes into multiple columns from the output of the Intersect above, but it would not pivot multiple point attributes without a lot of effort.
