Thanks for the full background on the situation! I agree with everyone here, but wanted to provide you what we do at TriHealth:
1. We do have a Facebook page specifically for employees, and it is public. We use this to showcase our culture and also remind employees to do things like annual training. However, we do know that we cannot require our employees to be on Facebook or "like" our page, so it just serves as another channel for our employees to stay connected. We do not solely rely on this for messaging. Also, we do not post these messages to our public corporate account, because as you said, most people who "like" that page are our patients/the community, and they don't need to see employee reminders. We also have a Careers FB page to post things like job openings. We rarely post anything like job openings to either of the other main pages, sometimes we post about large career fairs.
2. Weekly email from our CEO. This includes one main message as well as small 1-2 sentence blurbs about other announcements that then link to our intranet.
3. We post the latest news on our intranet and we have an automatic email every Wednesday at 6 am that goes to all employees with the stories posted from the last week. Between this email and the email from our CEO, we try to limit all other one-off emails if we can help it. Also, our news stories on our intranet can be seen publicly so we can link to them on our employee Facebook page. But only our news stories can be seen, no other pages can be viewed publicly without logging in.
Hopefully because all of us here are in agreement, you can use this as a business case not to include those messages on your normal FB account, but there are alternatives 🙂