WordPress Built In Dialog Box For My Plugin

This can be done using a front-end developer’s skills.

What i achieved through the customization is as follows.

Through the following code:

<?php add_thickbox(); ?>
<div id="my-content-id" style="display:none;">
  <link rel="stylesheet" href="https://code.jquery.com/ui/1.11.4/themes/smoothness/jquery-ui.css">
  <script src="https://code.jquery.com/jquery-1.10.2.js"></script>
  <script src="https://code.jquery.com/ui/1.11.4/jquery-ui.js"></script>
  <script>
  $(function() {
    $( "#tabs" ).tabs();
  });
  </script>

<div id="tabs" style="">

  <ul>
    <li><a href="#tabs-1">Insert Edit/link</a></li>
    <li><a href="#tabs-2">My Second Tab</a></li>
  </ul>
  <div id="tabs-1">
     <p>
          This is my hidden content! It will appear in ThickBox when the link is clicked.
     </p>
  </div>
  <div id="tabs-2">
    <p>Morbi tincidunt, dui sit amet facilisis feugiat, odio metus gravida ante, ut pharetra massa metus id nunc. Duis scelerisque molestie turpis. Sed fringilla, massa eget luctus malesuada, metus eros molestie lectus, ut tempus eros massa ut dolor. Aenean aliquet fringilla sem. Suspendisse sed ligula in ligula suscipit aliquam. Praesent in eros vestibulum mi adipiscing adipiscing. Morbi facilisis. Curabitur ornare consequat nunc. Aenean vel metus. Ut posuere viverra nulla. Aliquam erat volutpat. Pellentesque convallis. Maecenas feugiat, tellus pellentesque pretium posuere, felis lorem euismod felis, eu ornare leo nisi vel felis. Mauris consectetur tortor et purus.</p>
  </div>
</div>
</div>

<a title="<h2 style="padding:0.5em;">My Custom Popup<h2>" href="#TB_inline?width=600&height=550&inlineId=my-content-id" class="thickbox">View my inline content!</a>    

Add Css code as follows:

#tabs
{
height:100%;width:100%;border:none;padding:0 !important;

}

.ui-widget-header {
  border: none !important;
    background:none !important;
}

.ui-tabs .ui-tabs-nav li {
  }

  #TB_ajaxWindowTitle{
      color:red;
  }

  #TB_title{

      height: 4em !important;
  }

Not the exact structure you want but near to it.

An exact match with the styling like the media box can be obtained using css and jquery.