Usually duplicate benenfits are not permitted. The question is jurisdiction specific and it also depends on the type of workers' comopensation benenfit you are receiving, ie. temporary or permanent. Consult an attorney in your State.
Generally speaking, workers' comp benefits are available only to those with disability related to a work accident. Unemployment compensation benefits, on the other hand, require the recipient to certify that s/he is ready, willing, and able to work. Obviously, these two concepts are incompatible. So, it is possible that receiving both checks at the same time is not lawful; but, you did not provide enough facts to be certain.
If your father has questions specific to his situation, he should contact an attorney.
Ken Schwartz, Esq.