Regular Expressions - How to Delete Two Lines, If one contains X?

So I have a file and need to delete all instances that contain a certain string in the first line. Also Each line below the line that contains that string should also be completely deleted (no matter what it is). How do I make this happen?

Now obviously the expression for finding that first line is:

^.*STRING.*$

After that I'm stuck.

In other words I need to delete TWO lines and the first line contains my string.

 

Or alternately I could delete the line that is below the blank line. How?