Underinsured refers to various degrees of being insured for some real risks and uninsured for others, at the same time.

Underinsured
Who Are the Underinsured?
New estimates of the underinsured younger than 65 years.
How many are underinsured? Trends among U.S. adults, 2003 and 2007.
Out-of-pocket health spending and the rural underinsured.
Gaps in vaccine financing for underinsured children in the United States.
Delays in cancer diagnosis in underinsured young adults and older adolescents
Race and Ethnicity and Breast Cancer Outcomes in an Underinsured Population
Affordable Care Act reforms could reduce the number of underinsured US adults by 70 percent
Why is our population of uninsured and underinsured persons growing? The consequences of the "deindustrialization"of America