You can always shop for coverage on the marketplace, but your family members may not be eligible for tax credits to help pay the premium. When people are eligible for employer-sponsored coverage, they can only qualify for marketplace premium tax credits if the employer-sponsored coverage is unaffordable. The way this is calculated, coverage is unaffordable only if your cost for coverage for a single person under the employer plan is more than 9.86 percent of your household income in 2019 (for 2018, it was 9.56 percent of household income). So although you may feel your family coverage is unaffordable in practical terms, it is considered technically affordable.
If your family members end up uninsured because family coverage is unaffordable, they may qualify for an exemption from the tax penalty to have health insurance or the “individual mandate.” (26 C.F.R. § 1.36B-2(a); IRS, Rev. Proc. 2018-34.)