Is it normal for my child to prefer his father over me?

Yes. Sometimes it can seem like dad can calm a crying baby better than mom. This could be because your baby associates you with feeding and when they are crying they may smell the milk and think they are hungry, making them harder to soothe. When dad holds them they forget about this and calm quicker.
Yes. You worrying about whom your child likes more is probably one of the things driving the child away. Children feel happier with happier people. On second thought, most people feel happier with happier people. Look for ways to derive joy from your child's closeness with his/her father, and your own closeness will grow.