How to set border to <tbody> element?

Add:

table {border-collapse: collapse;}

FIDDLE

Add display:block to your tbody style. Try this

tbody{
    display:block;
    border: 2px solid black;
    border-collapse: separate;
    border-spacing: 4px; 
}

You can test it out on this fiddle

Use box-shadow instead of border. It works no matter which value of border-collapse was applied. In addition, you can also apply border-radius to it.

tbody {
  box-shadow: 0 0 0 1px black;
  border-radius: 5px;
}

<table>
  <thead>
    <tr>
      <th>Firstname</th>
      <th>Lastname</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Jill</td>
      <td>Smith</td>
    </tr>
    <tr>
      <td>Eve</td>
      <td>Jackson</td>
    </tr>
  </tbody>
</table>