we share a photo drive over our wireless router network
Bridge is not designed for use over a network, there are many threads about network usage in this forum, try also a search for 'The digital Archivist'. It seems sometimes seems possible but needs a lot of discipline.
In basic when you add a keyword to a file it saves in the XMP data in the file itself. Bridge has its own cache file in the user library and also in this user library there is a folder called 'application support' containing user specific settings like the keyword list that you have used on your Mac. When your husband adds a keyword to the list it is not automatically appearing in your list. If a file contains a keyword that is in the file but not in your list it appears as 'italic', with right click mouse menu on this word you can choose to make it persistent and then it is in your list and looks normal.
Although I have no experience with network shared disks I think it might be possible for you to find the keywords but as said not sure. You need to index the disk first for each Mac. This mostly is done automatically but it can be activated also with the Find command (Edit Find or cmd+F) Inhere choose source (your network disk) criteria Keyword: contains / -the text you want to find-. Be sure to have both checkmarks for subfolders and non indexed files activated and do a search. This might take a while.
If one of you has added a lot of new keywords to the list it might also be wise to use the export key word list function (keyword tab menu top right in the panel). The other one should use the import function for that new list and you both end up with the same list.
As said, it needs discipline because Bridge is original meant for stand alone usage.
Another option is to use a dedicated DAM (Digital Asset Management) application but also not sure about network usage for the common apps. You might find more info at the site of Peter Krogh: