In D&D 5e, as a Pact of the Chain Warlock, I can choose an eldritch invocation that lets me speak in my own voice through my familiar called Voice of the Chain Master (PHB 111):
You can communicate telepathically with your familiar and perceive through your familiar’s senses as long as you are on the same plane of existence. Additionally, while perceiving through your familiar’s senses, you can also speak through your familiar in your own voice, even if your familiar is normally incapable of speech.
Healing word is a spell with only a verbal component (PHB 249):
Components: V
[…]
A creature of your choice that you can see within range regains hit points equal to 1d4 + your spellcasting ability modifier.
The description of verbal components in the rules of spellcasting (PHB 203) says the sound of my voice alone is what causes the magic of this spell to happen:
Most spells require the chanting of mystic words. The words themselves aren’t the source of the spell’s power; rather, the particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion.
Say my familiar is in another room, no matter how far away. Through my familiar's eyes, I see a target at 60 feet. From my familiar comes my own magic-infused voice. That particular combination of sounds, with specific pitch and resonance, sets the threads of magic in motion that travel to the target and heal it.
Is this possible?
Best Answer
No.
Consider that:
If you can argue that this is ALL that is needed to cast a purely verbal spell, then anyone or anything with a mouth can cast it.
Let's get more basic: suppose you don't have spell slots left to cast Healing Word. Will speaking the words that produce "the particular combination of sounds, with specific pitch and resonance" set the magic in motion?
It all boils down to the power to cast it, and I'm afraid your familiar does not have it.
Let's look more closely, then, at:
There is nothing in there that ever mentioned -even vaguely- casting of any sort.
The argument of specific-beats-general here is also invalid because "specific" also denotes "explicit" and there is nothing here that explicitly and specifically grants you the power to cast verbal spells through the familiar. This case is more of a general-beats-vague.
Finally, the Find Familiar spell states the times when a familiar can (sort of) cast a spell:
Voice of the Chain Master lacks similar text that lets you cast verbal spells through it, so the feature can't let you do that.