Postdoc before PhD completion
Groups seeking postdocs will absolutely consider you as an applicant before you have completed your PhD. They will, however, want to be certain that you have completed the entire process and all its requirements prior to officially beginning your new job, as the comments above have said. Be as honest with them as possible about when you expect to finish.

Universities will vary in terms of how they expect you to prove you've completed your PhD: some will accept official letters while others will want a photocopy of your physical degree (I was asked for the latter and found it rather, er, surprising). Luckily, none of that is likely to happen during an interview.