Allow and encourage the person with borderline disorder to attempt to bring their response levels in line with the situation at hand. This may require that you give them a little time alone to collect themselves. Then it may be possible to more calmly and reasonably discuss the relevant issues.
In addition, do not be hesitant to express your feelings freely and openly, but with moderation. Recent research suggests that caring involvement with your loved one with borderline disorder is associated with better outcomes than a cool, disinterested approach. Stay involved.