Line break in multipart rectangle node with align specification

You could simply use a \parbox. You still could use \centering for the alignment, if desired. Furthermore it's recommended to use \tikzset instead of \tikzstyle.

\documentclass[10pt]{book}
\usepackage{tikz}
\usetikzlibrary{shapes.multipart}
\tikzset{umlclass/.style={
    draw=black,
    fill=yellow!16,
    rectangle split,
    rectangle split parts = 3,
    rectangle split part align={center,left,left},
    execute at begin node = \ttfamily,
}}
\begin{document}
\begin{tikzpicture}

\node[umlclass]{
    \parbox{2.4cm}{\centering
      <<interface>>\\
      class}
    \nodepart{second}
    +attribute
};
\end{tikzpicture}
\end{document}

The very good comment of egreg, to use a tabular to not need to know the width:

\node[umlclass]{
    \begin{tabular}{@{}c@{}}
      <<interface>>\\
      class
    \end{tabular}
    \nodepart{second}
    +attribute
};

You have to supply align=center to the general node options, as the first node part isn't treated like the others. The rectangle split part align option does apply to it, but only affects the box that uses the align option internally (which is also the reason \\ hasn’t the expected effect).

That means that one need to specify align=center and rectangle split part align={center,…}

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes.multipart,positioning}
\tikzset{
    umlclass/.style={
        draw=black,fill=yellow!16,rectangle split,rectangle split parts = 3,font = \ttfamily},
    umlclass -c/.style={
        umlclass,align=center,rectangle split part align={left}},         % = left,   left, left
    umlclass -r/.style={
        umlclass,align=right, rectangle split part align={left}},         % = left,   left, left
    umlclass +/.style={
        umlclass,align=center, rectangle split part align={center,left}}} % = center, left, left
\newcommand*{\umlclasscontent}{<<interface>>\\class\nodepart{second}very long attribute\nodepart{third}method()}
\begin{document}
\begin{tikzpicture}
\node[umlclass -c]           {\umlclasscontent};
\node[umlclass -r] at (0,-3) {\umlclasscontent};
\node[umlclass +]  at (0,-6) {\umlclasscontent};
\end{tikzpicture}
\end{document}