Intertext like command in enumerate environment?

Use the enumitem package and two separate enumerate environments, adding resume as option to the second environment.

\documentclass{article}

\usepackage{enumitem}

\begin{document}

Some text.

\begin{enumerate}
\item First item of enumerated list.
\item Second item.
\end{enumerate}

Some explanatory text.

\begin{enumerate}[resume]
\item Third item.
\end{enumerate}

\end{document}

Here is a custom command, \enumeratext, which works like \intertext, it does not require enumitem:

\newcounter{saveenumerate}
\makeatletter
\newcommand{\enumeratext}[1]{%
\setcounter{saveenumerate}{\value{enum\romannumeral\the\@enumdepth}}
\end{enumerate}
#1
\begin{enumerate}
\setcounter{enum\romannumeral\the\@enumdepth}{\value{saveenumerate}}%
}
\makeatother

Example:

\documentclass{article}

\newcounter{saveenumerate}
\makeatletter
\newcommand{\enumeratext}[1]{%
\setcounter{saveenumerate}{\value{enum\romannumeral\the\@enumdepth}}
\end{enumerate}
#1
\begin{enumerate}
\setcounter{enum\romannumeral\the\@enumdepth}{\value{saveenumerate}}%
}
\makeatother

\begin{document}
Here is a list:
\begin{enumerate}
\item Something,
\item some other thing,
\item and more;
\enumeratext{Some intertext}
\item let's continue,
    \begin{enumerate}
        \item here is a sublist,
        \item some stuff,
        \enumeratext{more intertext}
        \item yet another stuff.
    \end{enumerate}
\item last thing.
\end{enumerate}

\end{document}

Update: Now works for lower level list.

I achieved the task by just putting \item[] instead of \item in front of the inter text