Short term disability insurance is available here, and as I remember the cost isn't great for a young couple but to be honest I haven't really looked at it too closely because it's something I could handle by myself if it happened and when that's the case, I don't consider insuring. Long term disability is included as part of our Social Security package. If you have a few years of work history and become disabled for more than a year, then you become eligible for a SS retirement payment. Your wife and minor children also recieve what I think is half of your payment for each. A wife, two children, and your payment would end up doubling the amount you would recieve. I'd guess if you had a moderate level of income during your work history years, you might be looking at about $4,000 / month in just SS. SSI might add more to that, especially if minor children were involved. After two years of disability, you'd become eligible for Medicare coverage to take care of your health insurance needs and that could be a major expense as a result of what caused your disability.
SS is also quite generous to surviving spouses and minor children, in the event of death of the head of household is his work history was enough to warrant a payment.