Passworded page still showing info

I am trying to set up a password protected blog for my company and I need some help.

When I password the page, but not the post, I can still see everything. When I password the post, but not the page, I see the headings that tell me it’s protected.

What I want is for them to be able to see nothing except a login box until they enter the password. Is this possible without using a plugin of some sort? If not, any plugin recommendations? Do I need to have a separate page where they log in and then get redirected to the blog itself?