Background: Reduced funding to public health care systems during economic downturns is a common phenomenon around the world. The effect of health care cost on family members of the patients has not been established. This paper aims to explore the relationship between affordability of health care and vulnerability of family members to distress levels. Methods: Data of a total of 262,843 participants were obtained from 17 waves (1997–2013) of the United States National Health Interview Survey. Multinomial logistic regression was used to investigate psychological distress level as a result of having family members who experienced unmet medical needs due to cost. Results: Among participants without family members who experienced unmet needs for medical care due to cost, risks of having ‘moderate’ (score of 5–12) or ‘serious’ (score of 13 or above) level of psychological distress were 1.0% and 11.5%, respectively. Risks of having ‘moderate’ or ‘serious’ level of psychological distress were 3.1% and 23.4%, respectively among participants with family members who experienced unmet needs. The adjusted relative risk ratio of ‘moderate’ and ‘serious’, as compared to ‘normal’ level of psychological distress, were 1.58 (95% confidence interval: 1. 47–1.69) and 2.09 (95% confidence interval: 1.78–2.45) if one’s family members experienced unmet medical needs. Conclusions: Unmet medical needs due to cost increases risk of distress levels experienced by family members. Careful planning and adequate funding to public health care system could be implemented to prevent any unnecessary detrimental effect on mental health among family members of the unwell and any further increment of the prevalence of mental illnesses. This recommendation aligns with the World Health Organization Mental Health Action Plan 2013–2020.