You can make a macro to have on your alt (healer) and have it heal your main (warrior). Something like:
/cast [target=focus-target-target] HealSpell
That should heal whoever the main's mob is beating on (whoever has aggro).
Then just put that on a key that your main isn't using. Then use a key broadcaster (like HotKeyNet), to send whatever keys you push on your main to your alt.
Your main presses key "choose one" and your alt presses same key and does macro "Heal". Bam, healing in the background and no need to switch to the other screen.
Same works even if more than one person in your party, the macro just heals whoever has aggro. Doesn't even matter if the person isn't in your party (BG/PVP).

Hope that helps and good luck.