Is it permissible to use medical insurance cards for the family, and does the ruling differ if the insurance premium is paid by the company or by the resident?

If the insurance is compulsory, or if there is a Shariah-compliant Islamic insurance company (cooperative insurance), then there is no harm in benefiting from it. However, if it is with a commercial insurance company, it is not permissible to benefit from it except to the extent that was deducted from you or paid by the company.