You can have one relationship or multiple relationships.
In your example, the context needs to be clearer:
Our relationships with [the/our/(zero)] parents..... General statement - could be referring to the relationship between teachers and parents in a school setting OR human relationships in the family in general.
Our relationship with our parents - Could be either a general statement about human relationship in families, or a specific statement about "our" - my siblings and me - relationship with our parents.
Student or Learner