Severance and unemployment, do they overlap? - any advice?

I was offered severance of 8 weeks after being let go as an accountant and I am unsure how it affects benefits. Any experience at all would help. 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 last year, and it settled down once I kept a simple log of every call and form.