Merge lines at endpoints, yet still be continuous

[Javier_JovannyLeija]

I've created a sidewalks/walkways network but I'm having issues intersecting lines. What I'm trying to achieve is for the lines to split at intersections, but yet be continuous; as in, I do not want one line over the other, I would like for them to show as connected and continuing. I've provided an image if it helps.

[DanPatterson]

visually, I would just set the outline to match the fill color.  What is it currently set at?