Technically, your mother does not claim her husband as a dependent. She files a joint return with him and that precludes you from claiming him as a dependent. In order for you to claim him as a dependent, your mother must file as "Married Filing Separately (MFS)". You mother does not need to have provided more than half his support to file as Married Filing jointly (MFJ). Just being legally married is enough. They do not have to live together.
