Wikipedia: cognitive dissonance is the mental stress or discomfort experienced by an individual who holds two or more contradictory beliefs, ideas, or values at the same time, or is confronted by new information that conflicts with existing beliefs, ideas, or values.
So yes it is an example of Cognitive Dissonance.
Belief number 1. "I trust my girlfriend."
Belief number 2. "My girlfriend is not trustworthy"
Belief number 1. "I like my girlfriend and I don't want to break up with her."
Belief number 2. "My girlfriend cheated on me, THEREFORE I should break up with her."
The first set is based on the individual's comfort with his girlfriend being monogamous. His girlfriend has displayed capability and desire to not be monogamous. Loving relationships are usually based on openness and trust- e.g. that both know the conditions and stick to them and discuss any changes. It looks like this initial understanding is missing and the preconceptions of monogamy have now be called into question.
The second set is based on a cognitive framework of how relationships should work that logically says that cheating means breaking up.