If your National Insurance contributions are up to date, you'll be entitled to receive Contribution-Based JSA for up to 6 months. It's NOT means-tested, so your husband's income will be irrelevant. However Contribution-Based JSA doesn't qualify you for other benefits, such as free NHS prescriptions or for SMI (= Support for Mortgage Interest).
If you remain unemployed for 6 months, your right to Contribution-Based JSA will cease. You can then apply for Income-Based JSA but that IS means-tested, so your husband's income will be taken into account when assessing your entitlement. If you qualify for I-B JSA, you'll then also automatically qualify for other benefits (including free NHS prescriptions and SMI).
Council Tax Benefit is available to any household with a low income, irrespective of their employment status of those within the household or any other benefits which they might be receiving.
Chris