First of all, you need to provide more details/requirements -- without that, we can all only generalize, turning this into more a guessing game than a meaningful exercise.
Having said that...
What you're asking for is usually described as a Portal (either Intranet/Extranet/both), Content Management System (CMS), Document Management System, etc. etc. There are literally thousands of free/open source solutions available, some of which have native "Gallery" modules and I'd say 99.9% have some 3rd-party contributed Gallery module as well.
There are also purpose-built CMS systems tailored to images such as Gallery which not only lets you view the images in an album/slideshow format that's typically used throughout the Web, but also download/upload/contribute through a Web interface or FTP; granular permissions can also be used to restrict certain images/albums/sub-albums to certain users/groups.
Unfortunately, most of these were built on top of Linux/Apache/MySQL/PHP (LAMP), and while you can run the "AMP" or just the "MP" of the stack on Windows, this may be beyond what you're capable/permitted/wanting to do.
For Windows, there's also SharePoint Services 3.0, which is a freely-available portal from Microsoft that tightly-integrates with Windows/Office, but provides limited support for other browser/operating systems, and would require testing on your Mac clients to ensure that it's doing what you want it to do.
Again for Windows, there's DotNetNuke, another open source/free CMS that's quite mature (been around for at least 7 or 8 years iirc) that can likely do what you want to do on the Microsoft platform: Windows/IIS/SQL(express)/.NET Framework. Not sure about Mac OSX interop, but I'd gather since it's based on ASP.NET and SQL (database authentication), it should be ok (save for any ActiveX specific functionality).
You never specified whether you need granular per-user/per-group/per-image permissions, but what might work for you would be vanilla IIS with directory browsing enabled and Integrated Windows Authentication (and appropriate NTFS permissions on the root directory/sub-directories), which will seamlessly integrate with any Windows domain machines, while prompting for an Active Directory username/password for your Mac users using Safari/Chrome/FireFox.
While not sexy by any means, this is pretty bulletproof: all major browsers will provide a folder-like structure in the browser, uploading/maintaining the files/directories for you (I'm assuming) the administrator, can be done from Explorer from within the server.