Severance and unemployment, do they overlap? (update)

I was offered severance of 11 weeks after being let go as a web developer and I am unsure how it affects benefits. There are 11 people counting on me, so I am trying to be careful. I have a mortgage and need to plan. Did you file straight away?

Rules differ by state. I called the claims line and asked directly, then wrote down the answer and the date.