Is there anything you can do with a Biology and Psychology double major?

I don't think that the two go together very well... As a biologist, you'll either find a job in field research, in a laboratory, or doing research at a university. In psychology, you'll either become a therapist or a social worker. (I'm sure there are other options for jobs in those fields but none that pair the two together) The only thing that comes to mind is a forensic psychologist, but I believe they profile criminals; the biology may come in handy to understand the science behind the forensic evidence, but really, there probably wouldn't be a need for you to do so. Besides, a double major is a lot of work, if you don't already have both, pick one and do well in it.

Well, if you become a scientist you will use the training in scientific inquiry you obtained from both fields to apply to your research. Even if you don't want to be a scientist, if you want to go to grad school, you ought to find a lab with interesting research and then get a Masters which can help you achieve your goals in industry. You can figure out more of what you want to do as you get your degree and talk to your advisor. Step one is really finding a lab with research you really like so you can get through your degree with the right training to have broad options,

You could do research in Psychology and focus on biological aspects such as sleep behavior which can include using mouse model systems and techniques from neurobiology to track the physiology of this behavior. There is a lab at University of Iowa that does this. If you join a biology lab psychology will be harder to incorporate but you can look around for labs in Biology departments that focus on Psychology. Avoid evolutionary psychology though since the field has a lot of work to do as far as incorporating actual evolution (unless you want to pioneer a model for more rigorous science in the field- right now most in the field rely heavily on a overly simplistic purely adaptation model that would never stand criticism in the biology field). If you do this I suggest taking lots of evolution courses in a Biology department (you can and are often encouraged to take relevant classes from other departments in grad school).