Lineup captions of figures horizontally

Question

I got these three figures side-by-side. All of the figures are in different sizes and I got different number of lines of text in the caption for each of the figures. My problem is that I want all of the captions (first row of the captions, "Figure 1:", "Figure 2:", "Figure 3:") to be lined up horizontally. *I put in an example image.

I know that with tables I'am able to use [t] as table-captions are above the table, but figure-captions are below the figure and by that it suddenly becomes alot harder for me to solve the problem as I'm not able to use [b].

\begin{minipage}{\textwidth}
    \begin{minipage}{0.2\textwidth}
        \begin{figure}[H]
            \centering
            \includegraphics[width = 1\textwidth]{f01.jpg}
            \caption{Myyyy teeeexxxxt}
            \label{f04}
        \end{figure}
    \end{minipage}
    \hspace{0.02\textwidth}
    \begin{minipage}{0.35\textwidth}
        \begin{figure}[H]
            \centering
            \includegraphics[width = 1\textwidth]{f02.jpg}
            \caption{My texty texttext}
            \label{f01}
        \end{figure}
    \end{minipage}
    \hspace{0.02\textwidth}
    \begin{minipage}{0.35\textwidth}
        \begin{figure}[H]
            \centering
            \includegraphics[width = 1\textwidth]{f03.jpg}
            \caption{Textytex[![enter image description here][1]][1]t of my text which is text}
            \label{f03}
        \end{figure}
    \end{minipage}
\end{minipage}

Answer 1

Note that using a floating environment like figure inside a minibox environment does not make sense. The way around makes sense.

caption.sty provides an undocumented macro \captionbox which comes handy for your use case:

\documentclass[a4paper]{article}

\usepackage{caption,graphicx,geometry}
\geometry{showframe}

\begin{document}

\begin{figure}[t]
  \centering
  \rule{\textwidth}{2pt}\par
  \vspace{1ex}
  \fbox{%
    \captionbox{Some caption text which is not so
      long\label{fig:one}}[.45\textwidth][c]{%
      \includegraphics[width=.2\textwidth,keepaspectratio]{example-image-a}%
    }%
  }%
  \hfill
  \fbox{%
    \captionbox{Some caption text which is now longer and therefore
      has more text\label{fig:two}}[.45\textwidth][c]{%
      \includegraphics[width=.3\textwidth,keepaspectratio]{example-image-b}%
    }%
  }%
  \par\vspace{1ex}
  \rule{\textwidth}{2pt}
\end{figure}

\end{document}

Answer 2

Cheat! ;-)

\documentclass{article}

\usepackage{graphicx}

\begin{document}

\begin{figure}[htp]
\centering

\begin{minipage}[b]{.45\textwidth}
\centering

\includegraphics[height=5cm,width=3cm]{example-image-a}

\begin{minipage}[t]{\textwidth}
\caption{This is a short caption on two lines}
\end{minipage}

\end{minipage}%
\hfill
\begin{minipage}[b]{.45\textwidth}
\centering

\includegraphics[height=3cm,width=3cm]{example-image-b}

\begin{minipage}[t]{\textwidth}
\caption{This is a long caption on three lines, I hope
this text suffices for the task at hand.}
\end{minipage}

\end{minipage}

\end{figure}

\end{document}

The minipage is bottom aligned, but its bottom is the top of the caption!