Cats can become jealous upon the arrival of a new baby. Reassure the cat you still love it by paying lots of attention to it. If the cat is often neglected it will add to it's resentment. There is a myth that cats will kill babies - that they will "steal" the baby's breath. The only thing the cat is interested in is the babies milk or formula, and the babies warmth. The cat may curl up next to the baby but it's unlikely to lie on top of the baby. Keeping the bottle out of the crib or bassinet, will keep the cat from chewing on blankets or licking the babies face.
Give a short loud yell, like that of an injured cat and pull your hand away. Never hit your cat, this only teaches it to fear you. Some people believe that limited hand play is alright but it may lead to unpredictable behavior. If the cat persists in biting, lightly dust your hand in cayenne pepper. It will stop biting immediately.
You may wish to keep your cat off your furniture or table. Because cats can jump, climb, and love to be in high places, this is not really practical. But you can train your cat to stay off specific furniture by covering it with tin foil when you leave the house, and using a spray bottle for when you're there and catch them in the act.