The easiest solution is probably to create a custom UnderLineTextView component deriving from TextView, override setText() and set the entire text as underlined, something like this (underline code from the link you referred to above):
@Override
public void setText(CharSequence text, BufferType type) {
// code to check text for null omitted
SpannableString content = new SpannableString(text);
content.setSpan(new UnderlineSpan(), 0, text.length(), 0);
super.setText(content, BufferType.SPANNABLE);
}
It's then just a matter of using your new component in the layout and setting the text as usual. The rest is handled automatically.
More info on custom components:
http://developer.android.com/guide/topics/ui/custom-components.html