If your company does not have an EAP, be the driving force for setting one up, even if it is internal to the company and managed by existing staff. Something is better than nothing in this area.
If your company has an EAP, HR is the advocate and often the conduit of information on EAP. Be a non-stop EAP recommendation machine for your staff. If you are doing it right, they will interrupt your flow because they remember the last time you talked to them about it. EAP should be as common of a topic of conversation with you as the company's values and mission.