"Dividers" with TikZ

Like this?

I in above image consider your (rather simple) image:

\documentclass{article}
\usepackage[showframe,% only for test page layout
            margin=30mm]{geometry}
\usepackage{tikz}
 \usetikzlibrary{positioning, calc, shadows}

\begin{document}
    \begin{figure}%[ht]
\centering
    \begin{tikzpicture}[
    node distance = 7mm and 4mm,
every node/.style = {font=\bfseries\itshape},
   chapter/.style = {rectangle, draw, semithick, rounded corners,
                     text width=44mm, minimum height=11mm, align=center,
                     fill=white, drop shadow},  
        ys/.style = {yshift=-7mm}         
                        ]
\draw[thick] (0,0)  coordinate (A1)
                    node[below right] {Preliminaries} 
                    -- + (\textwidth,0)
                    coordinate (B1);
\node (ch1) [chapter, below=of $(A1)!0.5!(B1)$]         {Introduction};
\node (ch2) [chapter, below=of ch1]                     {Background};
\draw[thick] ([ys] A1 |- ch2.south)  coordinate (A2)
                    node[below right] {Problem states}
                    -- + (\textwidth,0)
                    coordinate (B2);
\node (ch3) [chapter, below  left=of $(A2)!0.5!(B2)$]   {State of the Art};
\node (ch4) [chapter, below right=of $(A2)!0.5!(B2)$]   {Building of Theory};
\draw[thick] ([ys] A1 |- ch3.south)  coordinate (A3)
                    node[below right] {Solution}
                    -- + (\textwidth,0)
                    coordinate (B3);
\node (ch5) [chapter, below=of $(A3)!0.5!(B3)$]         {My New Theory};
\node (ch6) [chapter, below=of ch5]                     {Validation of the Method};
\draw[thick] ([ys] A1 |- ch6.south)  coordinate (A4)
                    node[below right] {Conclusion}
                    -- + (\textwidth,0)
                    coordinate (B4);
\node (ch7) [chapter, below=of $(A4)!0.5!(B4)$]         {Discussion and conclusions};
\node (ap1) [chapter, below  left=of ch7]               {Appendix A};
\node (ap2) [chapter, below =of ch7]                    {Appendix B};
\node (ap3) [chapter, below right=of ch7]               {Appendix C};
\end{tikzpicture}
    \caption{Structure of the thesis}
\label{fig:structure-of-the-thesis}
    \end{figure}
\end{document}

If you draw all the boxes first you can use current bounding box to get the left and right borders of the graphics.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[
  TestBox/.style={draw,minimum width=3cm,minimum height=3em,rounded corners=2mm}]
  \node[TestBox] (A) {A};
  \node[TestBox,below left= of A](B){B};
  \node[TestBox,below right= of A](C){C is a bit longer than the other boxes};
  \node[TestBox,below=of $(B.south east)!0.5!(C.south west)$](D) {D};
  \node[TestBox,below=of D](E) {E};
  %%
  \coordinate(BBw) at ($(current bounding box.west)+(-5mm,0)$);
  \coordinate(BBe) at ($(current bounding box.east)+(5mm,0)$);
  \coordinate(Level1) at ($(C.south)!0.5!(D.north)$);
  \draw (Level1 -| BBw) -- (Level1-|BBe) node[pos=0,anchor=north west]{Label of line};
\end{tikzpicture}
\end{document}