You couldn't share the same photo stream unless you used the same primary iCloud account on your devices. You could do this and still keep your iCloud mail, contacts, calendars, notes an reminders separated by keeping your personal accounts as a secondary accounts on your devices. But you would end up sharing the same bookmarks, documents and data for iCloud-enabled apps; and would have to back up to the same account. This is because these are only supported in the primary account.
A better solution might be to keep your accounts separate, and then add your photos to shared streams and invite each other as subscribers. It would require you to manually add your photos to the shared streams but it would allow you to keep everything else as it is now. This explains how to create shared streams: http://help.apple.com/icloud/#/mmc0cd7e99.
On your last question, you can't view photo stream photos on icloud.com if that's where you are looking.