If your husband does not have ILR, Indefinite Leave to Remain, he is NOT eligible for ANY public funds at all. That includes 'benefits'. The website
www.dwp.gov.uk can give you a list of everything that's considered a public fund. Falling ill does not change a person's visa status, or his entitlement to benefits. It's just bad luck, unfortunately.
YOU, as a British person, can claim what you like, however, on your own and on your own income. For example, you can claim housing benefit in your name, or top up a low income with tax credits, council tax benefit, etc. Since you'd be the sole earner, these benefits will take this into account.
A trip to the Job Centre may be just the thing, since many benefits are now administered from here.