Communicate your concerns to your partner. Ask your partner to stand up for you if needed, and make sure that your partner doesn’t tolerate any criticism or contempt directed at you from their parents.
Their parents may be surprised at first, but they’ll come to accept the change in attitude and may begin to soften their way of speaking to you.
The same strategy applies if your partner is concerned about your parents, so ask them what you can do to help defuse a difficult situation.
Remember, you both are on the same team.