Spouses and unmarried children under the age of 21 can receive a so-called derivative I-visa. The spouse does not have permission to work with this visa. It is not possible to obtain a work permit with a derivative I-visa (which is different from the L-1or E-1/E-2 visas).
Children may also not work, but they can attend high school or university.
IMPORTANT: unmarried or same-sex partners do not receive a related status, the latter even if they are married under foreign law or US state law. They will have to apply for their own visa.