Keep Windows Users Out of Unix Shares?

We have a Celerra NX4. Right now, the admin in charge of our filers has 2 shares configured. One "Windows" and one "Unix". Users are supposed to access the "Windows" share from Windows machines, and the "Unix" share from Linux machines. But Windows users can see and access the "Unix" share, and all of the files and folders have full access granted to "Everyone" by default. We do not want to have to keep up with Windows ACLs on the Unix share, and we definitely want to prevent Windows machines from accessing the Unix share, and vice versa.

So, is there a way to have a Windows-accessible share that Linux workstations cannot see/access? And is there a way to have a Linux-accessible share that Windows workstations cannot see/access? I imagine that these shares were created in some sort of mixed mode that should be able to be turned off. Would we need to re-create the shares, or can they just be converted? At the LEAST, is there a way to simply change the Windows share permissions on the "Unix" share so that Windows machines are completely denied access?

I am not the EMC admin here, but I am the Windows Server admin, so I may not be able to answer any questions about our EMC setup. I'm just looking for info to help out our EMC guys. Thanks!