Yes, calibre can do exactly what you want through virtual libraries and a bit of extra work on your part. Virtual libraries are a relatively new feature, but basically they're a way of displaying only a limited portion of your total library.
You can do this with tags simply by adding "his" or "hers" (or your names) to each book; using both tags for books that by some coincidence you both happen to like. Then you could do a
tags:"=his" search and all of your books, but none of your wife's, will be displayed; or vice-versa. You can save this search and re-use it (the field to the right of search) and virtual libraries (to the left of search).
Another way to handle this would be creating a custom column (Preferences>Add custom column) and entering something into the custom column. Once again, it can be his/hers/names/whatever works for you. The use of the search field and virtual libraries remains unchanged. You don't even have to use text, you could use icons (maybe a facial picture?) instead.
I would suggest taking a further look into virtual libraries, custom columns, and using calibre's search function. You could start in the
calibre manual, or download an ebook version of the manual. There are also dozens of topics in these forums addressing each of these issues.