Wrong \href anchor location

Here is a very mild alternative that provides the output you're after:

\documentclass{article}
\usepackage[margin=0.5in]{geometry}% Just for this example
\usepackage{tabularx,graphicx,hyperref}

\begin{document}

\begin{center}
  \renewcommand{\tabularxcolumn}[1]{>{\centering\arraybackslash}m{#1}}
  \begin{tabularx}{\linewidth}{@{}m{.2\linewidth}Xm{.2\linewidth}@{}}
    \includegraphics[width=\linewidth]{example-image-a} &
    \large\bfseries
    My University \par
    Institute of Science and Technology \par
    C O U N T R Y &
    \includegraphics[width=\linewidth]{example-image-b} \\ \\[1cm]
    &
    \href{http://www.example.com}{www.example.com}
  \end{tabularx}
\end{center}

\end{document}

The m-column specification is similar to a p-column, but vertically centres its contents (supplied by the array package which is loaded by tabularx).