I'm not sure I understand 100% what you're trying to achieve, but --- like this?
\documentclass{article}
\begin{document}
\begin{center}
\rule{0.4\textwidth}{1pt} \hfill \rule{0.4\textwidth}{1pt} \\
Text
\end{center}
\end{document}

This is what comes to my mind when I hear "two separated lines in the same line, and centered text below them" anyway.
EDIT:
Here's what I might do in order to put centered text under each line:
\documentclass{article}
\usepackage{tabularx}
\newcolumntype{Y}{>{\centering\arraybackslash}X}
\begin{document}
\noindent
\begin{tabularx}{\textwidth}{Yp{1cm}Y}
\cline{1-1} \cline{3-3}
Text 1 && Text 2
\end{tabularx}
\end{document}
(The Y column type is taken from @Huugo's answer here.) Using \cline is probably suboptimal, and I'm sure there's more elegant, better-looking or just plain simpler ways of achieving this; I'm no TeXnician yet! But it might get you started.

EDIT 2:
Here's another version that uses \hrulefill (which I hadn't known about until now!) instead of \cline, and adds a little space between the two lines of the tabular environment by supplying the \\'s optional parameter --- one ex, to be precise, adjust this to your liking.
Speaking of spaces, the gap between the two lines is currently set to one centimeter, and this can also be adjusted. What's more, if you want to make the whole tabular narrower, you can change its width from \textwidth to 0.8\textwidth or something along those lines. (You'll probably want to wrap it in a center environment again then, otherwise it'll be flush left.)
\documentclass{article}
\usepackage{tabularx}
\newcolumntype{Y}{>{\centering\arraybackslash}X}
\begin{document}
\noindent
\begin{tabularx}{\textwidth}{Yp{1cm}Y}
\hrulefill&&\hrulefill\\[1ex]
Text 1 && Text 2
\end{tabularx}
\end{document}

Hope this helps!