The most obvious relationship that is involved in this covenant is the relationship between the two married people.  They are making a covenant to stay together in an exclusive relationship for their lifetimes. 

A second relationship that is involved in many marriage covenants would be a relationship between each partner and his or her in-laws.  When a couple marries, each partner is becoming a part of the other’s family.  They are making a covenant to treat one another accordingly.

Since you use the term “covenant,” there is the implication that this is a religious agreement.  There is, then, also a relationship between the partners and God.  They are promising God that they will remain in an exclusive relationship for their lifetimes.