Sometimes people sabotage your goals because they may have to face that they have a weight problem and don't want to deal with it. They maybe doing this consciously or unconsciously. If your parents are usually loving and caring towards you may want to consider that the diet sabotaging is unconscious behavior.
Parents want to protect their growing children. They may think that you are eating in an unhealthy way that may potentially harm you. I would sit them down and show them that your "diet" isn't a "diet" but a healthy way of eating for life. Educate them about SparkPeople. You never know, they may join too.