Public health insurance is provided or subsidized in some way by the federal government. Medicare, Veteran benefits, and insurance provided to federal employees are all examples of public health insurance. Private health insurance, on the other hand, is provided by private companies. The CDC estimated that in 2017, 65 percent of Americans under age 65 were covered by private insurance.
But it's also worth noting that if they keep the employer-sponsored plan for the whole family, the premiums will almost certainly be payroll deducted on the pre-tax basis. On the other hand, if they opt to buy an individual market plan, the premiums would only be tax deductible to the extent that they (along with other medical expenses) exceed 10 percent of the family's household income, and assuming that the family opts to itemize their tax deductions (increasingly rare now that the Tax Cuts and Jobs Act has greatly increased the standard deduction).
Depending on the health insurance company, Texas individual and family health insurance rates for couples can be based on the age of the youngest person on the policy. Some couples with an age difference of several years may find they save money by applying for the same plan rather than individually. Couples that are only a few years apart might be able to reduce their total costs by applying for separate health insurance plans. If you decide to apply for a health insurance plan as a couple, make sure the plan you choose covers the benefits both of you need.