Figure and Table next to each other (memoir class)

The capt-of package provides the right solution with \captionof. Also caption provides it, but this package is not recommended with memoir; on the contrary, the trick performed by capt-of is compatible with this class.

\documentclass{memoir}
\usepackage[demo]{graphicx} % the demo option is just for the example
\usepackage{capt-of}

\begin{document}

\begin{figure}
\centering
\begin{minipage}[t]{.4\textwidth}
\centering
\vspace{0pt}
\includegraphics[width=\textwidth]{figure.png}
\caption{This is the caption for figure}
\end{minipage}\hfill
\begin{minipage}[t]{.4\textwidth}
\centering
\vspace{0pt}
\captionof{table}{This is the caption for table}
\begin{tabular}{cc}
1 & Item 1 \\
3 & Item 2 \\
4 & Item 3 \\
5 & Item 4 \\
5 & Item 5 \\
\end{tabular}
\end{minipage}
\end{figure}

\end{document}

The \vspace{0pt} commands are to ensure top alignment. Dispose of them as you wish.