Both J1 and J2 visa holders must possess valid qualified health insurance during their stay in the US. If your J1 health insurance is paid by your sponsoring organization you can purchase health insurance for your J2 dependants. There are some J1/J2 visa health insurance plans that require the J1 visa holder to purchase coverage. You can select from other J1/J2 plans that does not have this requirement and purchase coverage for your dependants alone.