What sort of jobs are available for a person with a science degree in psychology?

Your best bet is likely to talk to a career counselor in your college's placement department; they would have a better idea of what is available and hopefully some advice, as well as being more knowledgeable about the degree itself.  They usually have job listings and sometimes even career fairs, so should have more direct knowledge of what companies are looking for.

I don't quite understand the distinction you make in your degree; generally "a major in psychology" IS a psychology degree.  Psychology is generally considered a very soft science, bordering on humanities; it generally takes more advanced study to get a job in the psychology field itself, especially research, and there's not much direct application to business. You could go for teaching certification, or a business graduate degree, for example, to raise your appeal to the workplace.

Degrees are different in Australia - a major in psychology is step 1, if you wish to go further you need to do a PhD and then an internship to become a psychologist.

Otherwise it akin to having a BA - you cannot use the degree in the workplace, its just seen as a stepping stone