I have an account on mail.his.com, which hosts both his.com and hers.com - can I log on using my hers.com address?

Yes - mail.his.com hosts the his.com and hers.com domains, and if you have an account on mail.his.com you can use either domain for email or logging in to https://spam.his.com

Since https://spam.his.com 'unifies' aliases on Zimbra accounts, it will only create one quarantine for your mailbox, even if mail comes in both to yourname@his.com and yourname@hers.com, so you only have to check your quarantine in one place.