You can always shop for coverage on the Marketplace, but your family members won’t 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 9.5% of your 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 will not have to pay a tax penalty under the “individual mandate.”