This is not good for your son. What about your arguments is causing him to think he has to take sides. Is Daddy mean to Mommy? Are the arguments angry with finger pointing, shoving, loud voices? If so, work really hard at taming them down.
Arguments are inevitable and they can be helpful for a child if they are managed in a calm manner. Have disagreements with a resolution and without obvious anger.
When you're angry, call for a time out and make an appointment for when to discuss it. This will not only help your son feel loving towards both parents while feeling more secure but will also help the two of you more likely to reach an agreement after your anger has receded.
When you stop the argument by laughing at your son, you are telling him that he's responsible for your being able to stop your argument. You are putting him in a place of responsibility for your happiness.
You are describing an unhealthy environment for your son. He's learning to get angry at Daddy because Daddy is angry at Mommy. It's not fair to him at all. And it's teaching him that the way to resolve disagreements is to argue and then laugh without having resolved the issue that started it all.
And perhaps most important of all, this scares him. He's not able to feel as secure as you'd like for him to be.