Double line in header

package scrlayer-scrpage

Here is a suggestion using package scrlayer-scrpage. It defines layer page styles. There you can clone the layer that inserts the headsepline. Then you can shift the layer a bit and change the line width.

\documentclass{book}

\usepackage[automark,headsepline=1.5pt,markcase=noupper]{scrlayer-scrpage}
\clearpairofpagestyles
\ihead{\headmark}
\ohead{\pagemark}
\setkomafont{pageheadfoot}{\normalfont}

\DeclareNewLayer[
  clone=scrheadings.head.below.line,% clone this layer
  addvoffset=2pt,% shift it down
  contents={\KOMAoptions{headsepline=.5pt}% change the line width
            \GetLayerContents{scrheadings.head.below.line}},% use the same code as headsepline
]{scrheadings.head.below.secondline}
\AddLayersToPageStyle{scrheadings}{scrheadings.head.below.secondline}% add the layer to the page style

\usepackage{blindtext}
\begin{document}
\blinddocument
\end{document}

---

package fancyhdr

With package fancyhdr you have to redefine \headrule.

\documentclass{book}

\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\fancyhead[LE,RO]{\thepage}
\fancyhead[RE]{\nouppercase{\leftmark}}
\fancyhead[LO]{\nouppercase{\rightmark}}

\renewcommand\headrulewidth{1.5pt}
\makeatletter
\def\headrule{{\if@fancyplain\let\headrulewidth\plainheadrulewidth\fi
\hrule\@height\headrulewidth\@width\headwidth
\vskip 2pt% 2pt between lines
\hrule\@height.5pt\@width\headwidth% lower line with .5pt line width
\vskip-\headrulewidth
\vskip-1.5pt}}
\makeatother

\usepackage{blindtext}
\begin{document}
\blinddocument
\end{document}