I know. You can get both of them at same time.

At least in California, it is allowed do that. My hu*****and and many of his coworkers did so, and it's approved by EDD, because severance is not considered pay for the job. Actually if your company can provide an statement saying that you are qualified for the unemployment benefits, some people can even get unemployment benefits before the official termination date (but after their layoff notification date, because some companies give notice earlier than the actual termination date). Check it out with your company and the rules in your state.