Parenting style is one of the greatest stressors in a marriage, apart from money issues. Many couples are taken by surprise when they discover that they argue about the slightest things once baby arrives. And things can get pretty ugly. Partners take offence when one partner wants to parent differently, indirectly implying that their way is wrong. Leave egos out of the equation and realise that doing something differently doesn’t mean that your way is wrong. It's just not comfortable for your partner. Some styles of parenting may also conflict with the personality of the baby. You may want to be laid back and flexible but baby may demand something entirely different.
The first thing you and your partner need to do is come to the understanding that you want to work as a team. This one agreement alone can relieve a lot of stress in the marriage. Then you need to make the rules of how the team will function. It can be helpful if you actually sit down and write down the rules. Compose categories such as sleep, food, discipline, atmosphere in the home, baths, bottle washing, and other such chores. Then negotiate who and how these tasks will be carried out. Try to meet on middle ground. Remember that parenting is not so very different than other aspects of any relationship; it's all about give and take and compromise. If you can't come to a mutual understanding, then it's time to call in the experts, either a parenting coach or a therapist who can help you both work through these obstacles.