At the risk of being shot down I have to say this is maybe a huge fuss over something that shouldn't be fussed over quite as much. Before you immediately shoot me down give me a minute to explain!
Had he meant it and said it maliciously, or indeed thought about it and still chosen to say it then yes discipline him, fire him, whoever says it deserves it. But I have been utterly convinced that he genuinely did not mean to say it racially and maybe yes he should have picked a better phrase but he said it without thinking and he as soon as he had he apologied, had he been completely ignorant it may have been a different story. I think this women is milking it for all she can get as horrid as that sounds. Yes now she has lodged the complaint they need to investigate it further but he does not need to get fired for a mistake he apologised profusely for straight away.
I didn't want to delete any of your quote, but I'm just asking about the bolded part.
It doesn't sound like he did realise that he had said something offensive and apologised as soon as he said it. From the OP's posts, it wasn't until he was hauled on the carpet that he even realised that it was a word he shouldn't have used and then apologised. I would have thought he'd have had an "Oh my gosh" moment as the word came out of his mouth and apologised to those around at that time.
I also really dislike people who say "he can't be a racsit/homophobe/whatever - his best friend is Indian/gay/whatever". Not all racists/homophobes/whatevers walk around in KKK robes. Not suggesting that the OP's husband is a racist, but sending money to a charity and being friends with someone from India doesn't preclude him from being one (or acting as one).
For the record, though I think that he shouldn't have used the rhyme that he did and that it should not have a taken a call to the office for an apology to be issued (not directly to the woman, as he didn't know she would complain, but to whoever was there at the time - if the woman could hear the rhyme she'd have heard the apology), I don't see this as a sackable offense. In the absence of previous problems, I think it is an over reaction on the part of his superiors.
For future reference - just count to 16 next time (it's the number of "points" you get with the rhyme).