Do some research before approaching him whether or not you feel awkward about bringing it up. My husband was dead-set against it at first. But then through babysitting children and seeing what they are learning (or not), talking to people casually about what they do, showing how I'm teaching our oldest on a day to day basis and watching him grow, reading a couple articles for and against, his attitude changed. Knowing a coworker that he respected and finding out that they homeschool, his attitude changed some more. Then researching what are your choices in your area (curriculum vs public school vs private school)? Are there any homeschool "helps" in your area and if so what are they, how much do they cost, how would you work it in, etc? (By this I mean that in Keller, TX where we recently moved from, they have all kinds of great co-ops (my friend's wife is hispanic and she teaches several children (hers included) Spanish and another friend teaches those same children (hers included) art classes in her art studio. There is a local homeschooling center where you can go for questions, help, and even certain higher classes online. Some homeschool centers I've heard of have a real lab (for science classes, chemistry, etc), computers with software needed for some classes, etc. Lots of local places I went to would have "homeschool days" once a week or month: the place I used to take my son to gymnastics classes offered a special general P.E. class for homeschoolers, or for older kids a deal on gymnastics as an elective. Similar things were offered at a cheer school, a pottery place, a fitness center, Fossil Rim, a wildlife center, an astronaut museum, lots of museums would have a free day every week, all kinds of places! I even received an invitation to homeschool days for special field trips like a tour of the new Dallas Cowboy stadium, zoo, aquarium, etc. It was very easy for my friends to bring their older children to sit in on legislature meetings, court, etc for lessons in civics classes, and they also brought their children with them on voting days. The Dallas-Ft Worth area had endless SOOOO many museums of all kinds (art, modern art, sculpture, western, cowboy, theatrical, science/nature, general history, regional history, airplanes, cars, native american, whatever you can think of), playhouse/theaters, all kinds of things. I even heard of some homeschool baseball leagues, organized by age playgroups, stuff like that where children from families with similar mindsets or values could play together. See what your area has and what you can do with them. When we lived in DFW, we were seriously considering homeschooling for awhile because the options were so rich. Since moving, I think we will enroll our boys in a private school and do things with them on the weekends, because it is a lot more rural and a lot less to do. We will be taking family trips to towns like Charleston or Washington DC on weekends as we can, but the options just aren't the same. Perhaps you can still do a lot, but just need to dig deeper.
Once you have all your research, you can present it to your husband in an organized manner with a lot more confidence.
Another issue some have is "kids need social outlets". What are your options there? My son has friends in church, he joined a local awanas club at another church (ours didn't have that club), and just signed up for soccer. Is that enough? Does he need more? (My oldest, probably yes. He's extremely social and seems to thrive with others to interact with. Other children, it may be enough...my youngest seems more content to just chill, though he is in a mommy and me music "class").
Personally, I think that whether you homeschool or place them in a traditional school setting, as a parent, you are still primarily responsible for their education. Still undecided in where our sons are going for school, at least my husband and I are both in agreement about taking it a step at a time, and still doing good things together as a family, providing every opportunity we can. Instead of just reading history or civics or whatever, we can take them places. We can play games and bring them along with us so they can gain understanding in the everyday errands on how commerce, free enterprise, etc work. Etc, etc. I think it is SO important, no matter what you do, to teach your children how to learn and how to think, not just shove facts down their throats. I think that's where most schools are really failing. I would love to see more logic exercises and teaching children how to learn in our system. We can only go with our children so far. We need to empower them to get what they need on their own and think for themselves too.
But in answer to your question about approaching your husband: lay out your position in an organized manner. Think about what arguments may be able to come up against it, and write them down. Try to make sure you have an answer or suggestion for each argument you can think of, so you're acknowledging all sides. Are there things you should work on now and improve? (For example: probably harder to sell homeschooling to someone if you're all unorganized and can't get some basics done around the house like shopping or cooking. Not to downgrade a mom or say that we "have to" do those things perfectly all the time, but it's an argument that can be made: if you can't keep milk in the house and dinner isn't made half the time, how is it gonna be when you add more to your day? That kind of thing....keep it in mind and see if you can actually (realistically) handle it. Good luck to ya, whatever you guys decide for your family.