If you look in the disABILITIES FAQs thread, there are some places listed that rent wheelchair accessible vans with ramps and wheelchair tie downs. These are mores expensive to rent, buy he would not have to transfer at all, as he could roll his wheelchair right into the van.
Most cars and vans do have some ability to adjust the height of the seat, but depending on the vehicle, it might not have enough adjustment to meet your DH's needs. Some of the vehicles are just higher off the ground than others.
Even most small SUVs usually have the seat much higher off the ground than most cars. Some vans have seats higher off the ground than others.
I agree with peemagg that the Windstar or Town and Country are probably some of the lower vans.
I'd suggest looking at some of the rental companies and see what kind of vehicles they carry. I looked at Dollar, for example and found they have only mid-size SUVs listed - Jeep Liberty (or similar). That's a pretty high SUV.
For vans, they list Dodge Caravan (or similar). The problem is the "or similar", that you may not know exactly what you will get. I looked at Hertz and couldn't really tell what kinds of vehicles they rent.
I would suggest measuring the seat height of your car and then having your DH make an estimate of how much higher or lower would likely work for him. Even if the companies don't list an easy way to contact anyone for special needs, they should have someone who should be able to help you if you call with the seat heights and see what they have. After you know that, you might be able to go to a car dealer to actually see those models. Sometimes, the height might be OK, but the way things are arranged may not work. If you find one you think will work, call and ask if they can guarantee that type for you because of your DH's needs related to his disability.
I know there are several people who post on this board that are paraplegic. They might be able to give some better suggestions.