A style like this doesn't make much sense to me. You give up the one big advantage of a numeric style: unintrusiveness. Since you add the author and year the citation gets longer, and the numeric label doesn't add any further information that the author-year part can't give you (if done properly, of course).
That said, you can just add the name and year to the cite macro, but then we also need to move about the brackets.
\renewcommand*{\nameyeardelim}{\addspace}
\DeclareCiteCommand{\cite}
{\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\usebibmacro{cite}}
{\multicitedelim}
{\usebibmacro{postnote}}
\renewbibmacro*{cite}{%
\printtext[bibhyperref]{%
\printnames{labelname}%
\setunit{\nameyeardelim}%
\printfield{year}%
\setunit{\addspace}%
\printtext[labelnumberwidth]{%
\printfield{prefixnumber}%
\printfield{labelnumber}}%
\ifbool{bbx:subentry}
{\printfield{entrysetcount}}
{}}}
Note that this redefines the \cite command and not \textcite/\citet.
In total
\documentclass{article}
\usepackage[
backend=bibtex,
style=numeric,
natbib=true
]{biblatex}
\bibliography{biblatex-examples}
\renewcommand*{\nameyeardelim}{\addspace}
\DeclareCiteCommand{\cite}
{\usebibmacro{prenote}}
{\usebibmacro{citeindex}%
\usebibmacro{cite}}
{\multicitedelim}
{\usebibmacro{postnote}}
\renewbibmacro*{cite}{%
\printtext[bibhyperref]{%
\printnames{labelname}%
\setunit{\nameyeardelim}%
\printfield{year}%
\setunit{\addspace}%
\printtext[labelnumberwidth]{%
\printfield{prefixnumber}%
\printfield{labelnumber}}%
\ifbool{bbx:subentry}
{\printfield{entrysetcount}}
{}}}
\begin{document}
\cite{sigfridsson}
\printbibliography
\end{document}

\textcite{<key>}, but usually you don't mix Harvard and Vancouver. – Johannes_B May 01 '16 at 16:35citestyle=authoryearshould be enough. – Bernard May 01 '16 at 16:35