Even though director’s and officers are considered an insured under a general liability policy, it only provides coverage with respect to their duties as your directors and officers.
Directors and officers liability insurance (often called D&O) is liability insurance payable to the directors and officers of a company, or to the organization(s) itself, as indemnification (reimbursement) for losses or advancement of defense costs in the event an insured suffers such a loss as a result of a legal action brought for alleged wrongful acts in their capacity as directors and officers.
Such coverage can extend to defense costs arising out of criminal and regulatory investigations/trails as well; in fact, often civil and criminal actions are brought against directors/officers simultaneously. Intentional illegal acts, however, are typically not covered under D&O policies.