Severance and unemployment, do they overlap? - 10 months and counting

I was offered severance of 13 weeks after being let go as an event coordinator and I am unsure how it affects benefits. There are 13 people counting on me, so I am trying to be careful. I have a mortgage and need to plan. Who should I ask before signing?

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.