Is it permissible for my husband to use the free minutes, in excess of his work requirements, which are either rolled over to the next month or expire, knowing that the company has not specified how he should use them?

If the company permits the employee to use its phone for personal needs, or if custom dictates such use, then there is no harm in benefiting from it. However, if the company does not approve of this, or if custom dictates that it is not allowed, then it is impermissible to use it for personal purposes except with the company's permission.