Bibi, I'm a dog nut (I adore them and we've got three) but here's the thing - my sympathies are entirely with your DH. No reputable rescue or breeder is going to home a dog where an adult living there is so clearly unhappy about it. Why? In these circumstances, the homing is much more likely to break down and sooner or later, the dog will end up in a rescue. Yes, the dog would be primarily your responsibility but what happens if you are suddenly taken ill, or need to get a job, or one of the DC is taken ill? Who is responsible then?
Dogs smell, they are a financial drain (even with insurance), will outlast your children leaving home, make a mess, leave hair everywhere, tie you to the house, can bark, and need lots and lots of exercise every single day, rain or shine.
Let's talk about the money. If you're rolling in it, great, but for many families, especially in the current economic climate, cash is tight. Maybe your DH doesn't think the family budget can stretch to the full cost of the dog. As well as the cost of the animal, there's food, worming, vaccinations, bed, coats, collars, some breeds need professional grooming/trimming regularly, kennels when you go on holiday, maybe a change to the family car, and of course insurance. And even if you have insurance, alot of ongoing vet costs won't be covered, and don't forget you have to meet the excess on each claim.
If you really want a dog in your life, there are many, many ways of doing this that don't involve owning one. Volunteer with the Cinnamon Trust, and help an elderly or terminally ill person by walking their dog regularly. Contact your local dogs home or rescue - they are usually desperate to have the dogs in their care walked regularly. Help out at your local rescue kennels/dog charity - again, dog charities are desperate for people to help move dogs, volunteer, in so many different ways. Most of the dog charities I know would bite your arm off (metaphorically) if you turned up to help out regularly.
Another option is to become a foster home for a dogs charity, again they'd be keen especially since you have children. This might be an ideal way for your DH to see what the reality of actually living with a woof is like, with the happy thought that the dog will be going at the end of a relatively short period, and while it is with you, its vets bills and food are paid for by the charity.
This is about trust and respect, but also the dog (if you got one now) would be an innocent creature forced to live with an adult who did not want it there - I would never put any dog in those circumstances willingly.