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}

\part
takes an entire page.memoir
class provides options for styling the layout of the\part
-page, as described in section 6.4 of the manual.\part
not take a whole page, you need to make\chapter
not start on a new page too, assuming you have a\chapter
after every\part
.