You can use an existing float such as figure instead of minipage to hold your side by side figure and table.
\documentclass{article}
\usepackage{capt-of}
\makeatletter
%\let\ftype@table\ftype@figure
\makeatother
\begin{document}
\listoffigures
\listoftables
\clearpage
\begin{figure}
\begin{minipage}{.4\textwidth}XXX
\captionof{figure}{fff}
\end{minipage}\hfill
\begin{minipage}{.4\textwidth}\rule{2cm}{1cm}
\captionof{table}{ttt}
\end{minipage}
\end{figure}
aaa
\begin{figure}
\begin{minipage}{.4\textwidth}YYY
\captionof{figure}{fff}
\end{minipage}\hfill
\begin{minipage}{.4\textwidth}\rule{2cm}{3cm}
\captionof{table}{ttt}
\end{minipage}
\end{figure}
aaa
\begin{table}\rule{2cm}{7cm}\quad\rule{2cm}{7cm}
\caption{TTT}
\end{table}
aaa
\begin{figure}
\begin{minipage}{.4\textwidth}XXX
\captionof{figure}{fff}
\end{minipage}\hfill
\begin{minipage}{.4\textwidth}\rule{2cm}{1cm}
\captionof{table}{ttt}
\end{minipage}
\end{figure}
aaa
\begin{figure}
\begin{minipage}{.4\textwidth}YYY
\captionof{figure}{fff}
\end{minipage}\hfill
\begin{minipage}{.4\textwidth}\rule{2cm}{3cm}
\captionof{table}{ttt}
\end{minipage}
\end{figure}
aaa
\end{document}
Note however that while this works, LaTeX sees this as a figure while floating boxes around so only keeps it in sequence with figures this means that if some tables are on their own in a table environment they may float out of sequence with tables that are in a figure environment.
The end result is that the list of tables looks like

The simplest fix is to uncomment the commented line so that figures and tables are kept in the same sequence. This has the disadvantage that LaTeX won't then float any figure past any table so it gives less flexibility in the algorithm but it has the advantage of working and placing teh floats in the correct order as shown in the lists:

floatrowpackage, and it would be a good option, if my document class hadn't used thefloatpackage. I'm getting errors that say they're not compatible. – Jelle May 24 '13 at 11:58minipagewithfigure. – Torbjørn T. May 24 '13 at 12:02floatrowpackage is (nearly) compatible to the commands offered by thefloatpackage, you could replace thefloatpackage by thefloatrowpackage. – May 25 '13 at 05:09