login to separate WordPress sites with one user account


We have 2 separate WordPress sites.

One is a membership site, and the other is more of a public site. Our customers use the membership site for accessing resources. They also have a separate account on the public site where we have a directory plugin installed which they can use to list their location online.

As you would expect, we get a regular amount of confusion from our customers since they don't always realize that each site is separate and that they have separate accounts for each.

I'm wondering if there's a way to allow our customers to be able to sign on to either site with 1 user account? Or perhaps another creative way to work around the problem?