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

I was offered severance of 9 weeks after being let go as a line cook and I am unsure how it affects benefits. I have read a lot of threads here and could not find my exact situation. I have a mortgage and need to plan. Did you file straight away?

Thanks for writing this out. I went through something close to it 6 months ago, and it got easier once I kept a simple log of every call and form.