The house represents a goal to achieve. One important aspect of the American Dream is having a goal to achieve or a dream to begin with. Everyone has a goal to achieve otherwise you don't have something to look forward to.
Another aspect of the American Dream is the sense of togetherness. The two people represent being together with the ones who you care about and it is these people that will help you to achieve your goals in your dream. Being with people who care and support you is part of the American Dream.