ButterflyEffect is spot on.
From the dog's POV, you were warned. He considers you either a threat or that he is higher up in the whole scheme of things than you - ie he will take notice of your DH but will tell you to get lost. I suspect the latter. My immediate advice would be to heed the warning right now and secondly to take steps to be able to be in a position whereby the dog does not feel the need to do this.
A behaviouralist will address the dog's behaviour AND yours - that's not meant as an insult btw, just meaning that he/she will teach you where you are making mistakes and how to address them.
Opt for a qualified, registered behaviouralist, preferably taking a recommendation from someone you trust who has had personal experience of a particular one in your area. Perhaps the rescue would be able to point you to one, or another local erscue might?
Speak to the rescue the Grey came from for their advice - they should offer a lifetime's support. Which were they, btw, it may help? (Am a rescuer so know many rescues).
Also have a word perhaps with Trudy at Greyt Exploitations, someone I know personally. It's largely a campaigning group BUT Trudy is a star and rescuer of Greys herself, knowing a hell of a lot on the breed. Trudy's website is HERE and you'll find contact details for her there too, including her phone number.
Tony at Greyhound Action may also be able to put you in touch with someone suitable as will Kaye and her team at LurcherLink
By the way, dogs that bite should not get putdown. Those who meet the right rescuers do not get put down. Your DHs adoption contract should include a commitment to return the dog if for whatever reason, he cannot keep him. Should it come to that, please refer back to the rescue. Should they not be willing or able to help and you are unable to keep him (dog that is, not DH!), please post on Pets with my name in the title and I will find him a no-kill rescue place. It's what I do. WRT that, whatever you do, avoid the RSPCA at all costs, even if that's where the dog came from. Should this be the case please refer back to me, I'll explain all and help you find an alternative,
A quick look at Trudy's Greyt Exploitations website will demonstrate to even the most cynical what terrible existances Greyhounds often have prior to reaching rescue and why some Greys have issues. The very vast majority of issues can be ironed out, providing the humans involved are willing to understand and put in the effort.
it sounds like your DHs Greyhound is a very lucky boy today.