How to make send_headers hook work for admin

I’m trying to send a request headers for requests to the admin screens, but the hook “send_headers” appears to only fire for the blog itself, not the admin screens. Here’s the code I added to functions.php:

add_action( 'send_headers', 'add_header_xua' );
function add_header_xua() {
	header( 'X-UA-Compatible: IE=edge,chrome=1' );
}

Does anybody have any idea how I can add a custom response header for the admin screens? (I need to do this because our agency turns on compatibility mode in IE by default and I’m trying force everybody’s browsers to NOT run in compabitlity mode.) Thanks!