I moved to the US (Florida) 30 years ago to be a nanny for a relative's kids for three months as they relocated.
Obviously some things will have changed but here are some basics:
His employer will pay healthcare. This is standard and will cover the whole family. Insist it's in place day 1 because the little boy had to go to hospital with a minor injury in week 3 and they weren't covered at that point. The family sent the whole bill to the employer - who paid.
There will be a relocation allowance. This will cover storage in the UK (if you use it), shipping of furniture etc, airfares in Business Class when you fly out. They should also pay for you to go out and house hunt and should provide you with someone who has done scouting for you ahead of time. You may have to have temporary furnished accommodation for six weeks while you wait for the furniture - it comes by sea.
You'll need to take a lot of luggage (and most of your clothes) to last you while you wait for your belongings to arrive. The container was fumigated on arrival in the US, so you may want to think about shrink wrapping furniture and soft furnishings because of the risk of pesticide being in them.
Insist on two flights home annually. Employees generally only get two weeks' vacation so ask them to match his UK holiday allowance.
Schools. Like housing they should set up some visits for you ahead of time.You may want them to pay for a British or International school or a charter school (like private but cheaper). The US start school at 6 so their grades are one behind. Their Second Grade is Year 3.
Some of the schoolwork was difficult for the children because they didn't know the culture, so on being asked to fill in__man, one child wrote milk man (this was back when milk was delivered in the UK) and the US doesn't have milk men so that was a wrong answer. Pronunciation may also be a factor, so you may have to say things in an American accent to see which are the rhyming words in homework.
The children will probably have to take the pledge of allegiance at school every morning. They can ask to be excused but this may make them stand out more.
Company car. If your DH has a company car he'll need to insist on one in the US. This was a perk only for company Vice Presidents in the 1990s.
Everyone drives everywhere. Even from one end of a strip mall to the other. Walking to go somewhere is considered weird as it's done for exercise. Don't be surprised if you see walking trails in malls or parks and they're called hiking trails. Some people walk round the mall as exercise.
Working You may not get a visa to work or alternatively ask them to find you a job. This is quite standard when couples move and is easier if you're a doctor or accountant. If you can't get a working visa (which you should push for because it's not just 2-3 years), you can push for them to pay for you to get an MBA (this was offered to my relative's wife) or Masters or PhD.
If they want him to do the job they will pad the offer with lots of support and push for as much as you can. Also they should offer you both a 2-3 day trip to the area to see what it will be like before he says yes. He'll get shown the office etc and they'll show you other things on your own and with him.
I hope this helps.