Is it normal to inherit dreams?

Long ago, I once had a dream about me and my parents searching for my dog in the middle of a deserted city. When we found my dog, it was with this weird dog-like chimera creature and my dad tried to chase it away from us. It ran and jumped around trying to escape before it stopped right in front of me and stared at me for a second and then it ran away, leaving me frozen in shock/fear. I woke up quite shaken and told my mom about it. I described the creature to her and she became serious. She told me that when she was young/teenage, she dreamed of the exact same creature, so did my uncle, her older brother, and grandfather. She didn't know what it meant. I still remember the dream and creature clearly and it gives me the chills every time I think about it. Even so, I am curious to know what it means or if something similar has happened to someone else. It would be a great relief if someone could help me.