Here's one possibility, using the titlesec package; before each \section, some commands can be used: \undefds suppresses previous dates and subtitles; \sectiondate{<text>} assigns <text> as the date for the following \section, and \sectionsubtitle{<text>} assigns <text> as the subtitle for the following \section.
Since titlesec was used, somre restrictions apply (See About memoir and titlesec incompatibility). The code:
\documentclass[article]{memoir}
\usepackage[margin=3cm]{geometry}% just for the example
\usepackage[T1]{fontenc}
\usepackage[explicit]{titlesec}
\usepackage{xcolor}
\usepackage{textcase}
\usepackage{lmodern}
\usepackage{lipsum}
\makeatletter
\newcommand*\nameundef[1]{%
\expandafter\let\csname #1\endcsname\@undefined}
\newcommand\sectiondatefont{\normalfont\sffamily\itshape\bfseries\Large}
\newcommand\sectionsubtitlefont{\normalfont\sffamily\LARGE}
\newcommand\sectiondate[1]{\def\@sectiondate{#1}}
\newcommand\sectionsubtitle[1]{\def\@sectionsubtitle{#1}}
\titleformat{\section}
{\normalfont\bfseries\huge\sffamily}{}{0em}
{\colorbox{gray}{%
\parbox[t]{\dimexpr\textwidth-2\fboxsep-2\fboxrule\relax}{%
\vspace*{1ex}%
\@ifundefined{@sectiondate}
{}{{\sectiondatefont\@sectiondate}\\*}%
\raggedright%
\textcolor{white}{\huge\MakeTextUppercase{#1}}%
\@ifundefined{@sectionsubtitle}
{}{\\*{\sectionsubtitlefont\@sectionsubtitle}}%
\vspace*{1ex}
}%
}%
}
\newcommand\undefds{%
\nameundef{@sectiondate}\nameundef{@sectionsubtitle}}
\makeatother
\begin{document}
\sectiondate{March 15, 2013}
\sectionsubtitle{Test Subtitle}
\section{Test Section With a Title Spanning Two Lines}
\lipsum[4]
\undefds
\section{Test Section}
\lipsum[4]
\undefds
\sectiondate{April 23, 2009}
\section{Another Test Section}
\lipsum[4]
\undefds
\sectionsubtitle{Another Test Subtitle}
\section{Test Section}
\lipsum[4]
\end{document}
An image of the result:

\sectioninstead of\section*and add\setcounter{secnumdepth}{0}in the preamble, so that sections won't be numbered, but will go to the TOC nonetheless. – egreg Mar 18 '13 at 09:27