Severance and unemployment, do they overlap?

I was offered severance of 14 weeks after being let go as a customer-service rep and I am unsure how it affects benefits. I do not usually post, so bear with me. The agreement mentions a release and a payment schedule. How did your state treat it?

Thanks for writing this out. I went through something close to it 2 months ago, and it settled down once I kept a simple log of every call and form.