What you are dealing with is an artifact of the method reports are rendered in SSRS. The default rendering engine is MHTML. In HTML, there is no easy way to layer elements atop one another so that they render consistently (I understand that with some advanced CSS it can be done in certain circumstances, but that how a given browser will interpret it will cause inconsistent results).
If you have taken the effort to put your sub-report so that it is behind the lines in layout, Those lines should show up on top if you choose to render the report in PDF rather than the default layout. I just tested this in SSRS 2016 and it works, not sure if it will work the same in earlier versions, but there a number of features (newspaper columns, etc.) which don't render properly in MHTML, but do in PDF.