Here's a version using the titlesec package. I've made the \part and chapter styles identical, and roughly imitated the Conny style. You probably don't want to do exactly this, but it should be enough to get you started.
\documentclass{book}
\usepackage{lipsum}% for dummy text
\usepackage{titlesec}
\titleclass{\part}{top} % make part like a chapter
\titleformat{\part}
[display]
{\centering\normalfont\Huge\bfseries}
{\titlerule[5pt]\vspace{3pt}\titlerule[2pt]\vspace{3pt}\MakeUppercase{\partname} \thepart}
{0pt}
{\titlerule[2pt]\vspace{1pc}\huge\MakeUppercase}
%
\titlespacing*{\part}{0pt}{0pt}{20pt}
%
\titleclass{\chapter}{straight} % make chapter like a section (no newpage)
\titleformat{\chapter}
[display]
{\centering\normalfont\Huge\bfseries}
{\titlerule[5pt]\vspace{3pt}\titlerule[2pt]\vspace{3pt}\MakeUppercase{\chaptertitlename} \thechapter}
{0pt}
{\titlerule[2pt]\vspace{6pt}\huge\MakeUppercase}
\titlespacing*{\chapter}{0pt}{0pt}{40pt}
\begin{document}
\part{A part}
\chapter{A chapter}
\lipsum[1-2]
\end{document}

\parttakes an entire page. – Stefan Oct 04 '11 at 13:51memoirclass provides options for styling the layout of the\part-page, as described in section 6.4 of the manual. – Carsten Thiel Oct 04 '11 at 13:57\partnot take a whole page, you need to make\chapternot start on a new page too, assuming you have a\chapterafter every\part. – Alan Munn Oct 04 '11 at 15:12