Simply use one float environment with two minipages inside. Then use the normal \caption for the one float and \captionof{<other type>}{<caption text>} for the other. This needs either the caption or the capt-of package.
The issue with scheme from chemscheme is that it isn't a normal float but (by default) defined using floatrow which doesn't support code like above (I get a 'caption lost' error). The alternate definition over the float package doesn't work either because it always places the caption on its own and not part of the actual content, so it breaks out of the minipage.
I now found the following solution which undoes some stuff from the floatrow package and define scheme the same way as figure:
\documentclass{article}
\usepackage[demo]{graphicx}% 'demo' option only to not require actually images for this example file
\usepackage{capt-of}% or 'caption'
\usepackage{chemscheme}
\begin{document}
\makeatletter
\def\scheme{\@float{scheme}}
\let\endscheme\endfigure
\makeatother
\begin{scheme}
\begin{minipage}{.48\textwidth}
\includegraphics[width=\textwidth]{normalimage}
\captionof{figure}{My figure}
\end{minipage}%
\hfill
\begin{minipage}{.48\textwidth}
\includegraphics[width=\textwidth]{chemfig}
\caption{My chem scheme}
\end{minipage}%
\end{scheme}
\end{document}
However, putting \captionof{scheme} into a figure environment still doesn't work ('caption lost' error again).
You would recommend to wait until someone which knows floatrow better than me posts an answer.