Severance and unemployment, do they overlap? - what worked for you?

I was offered severance of 9 weeks after being let go as an accounts payable clerk and I am unsure how it affects benefits. There are 9 people counting on me, so I am trying to be careful. I have a mortgage and need to plan. How did your state treat it?

Thanks for writing this out. I went through something close to it 10 months ago, and it settled down once I kept a simple log of every call and form.