I looked into it seriously about a year ago and decided it wasn't the right thing for me (as a single person) to do at the time, so I don't know exact details, but this is what I do know.
There isn't just one "Social Security", there are a lot of different programs which have different qualifications. It's byzantine and can take a long time to get disability-based benefits. They're also pretty tough to get, especially for things like anxiety and depression, which (as debilitating as they are) are treatable. Income-based benefits like food stamps, Medicare, or housing subsidies are much easier to get, especially for families.
Your husband making money might make a difference depending on how much he makes, the cost of living in your area, and the size of your family. Just having some other income doesn't disqualify you, though. Even if you personally had a job you could still receive some benefit.
You should apply for everything you can, but I would guess that food stamps would be the quickest and easiest to get, and will probably make a big difference on your family's situation.