Yes they can be kept in the home aquarium, unfortunately they are very delicate and require a hobbyist with a lot of experience. If you are a beginner or haven't been keeping aquariums for a few years I would suggest not jumping into keeping them. They live about 2-4 years.
Seahorses, like many salt water fish are wonderful pets. They live anywhere from 2-5 years. Caution, care of a salt water tank requires an investment of time and money, and is not a cheap hobby by any means.