I never knew that there was Linux support for SQLServer, but it turns out that there is a JDBC 4.0 driver for it that can be used in GeoServer.
From the download, put sqljdbc4.jar in the tomcat/lib directory if you only want JNDI connections, or in the GEOSERVER/WEB-INF/lib directory if you want connections that can be defined in GeoServer as well.
Download the sqlserver plugin for GeoServer, and put the jar file (in my case gt-jdbc-sqlserver-9.3.jar) into the GEOSERVER/WEB-INF/lib directory.
Now restart Tomcat (or just the GeoServer webapp if you don’t want JNDI connections). Now create a new store. Be sure to open up port 1433 on your Windows firewall, or otherwise GeoServer can’t reach it.