I'm interested in both Psychiatry and Neurology, but from what I've gathered, it's sort of useless to do a dual residency (6 to 7 years) and get double board certified. Realistically, you'll have to practice one discipline or another. Even if you went private practice, it would be difficult to keep up with both patient populations and be effective.
If you want to be "in between" both specialties where you see patients that exhibit symptoms of both or you want to be a liaison between both specialties, you're much better served by doing a 1 year fellowship after your residency (4 years). As the previous person pointed out, this would make you either a Behavioral Neurologist or Neuropsychiatrist. They both do the exact same fellowship both mixed in similar groups, and as far as I understand, they call themselves "Behavioral Neurologists" if their residency was in Neurology and "Neuropsychiatrists" if the the original residency was in psychiatry.