If you're willing to store your paswords encrypted-but-publicly-available, it's trivial:
Obtain a password manager such as KeePass, Lastpass, Password Safe, or a number of other options.
Create a password database containing your common passwords. (Naturally you would follow standard procedures to create a master password for the database, as the database is encrypted with a key derived from the master password.)
Store the encrypted database in a location commonly accessible to both of you. Dropbox is fine, since the database is encrypted, but other cloud services work too.
Both of you share the master password to the database.
Do note that this does NOT provide security against one of you changing the database master password. Given that you're looking to share passwords this way, it shouldn't be an issue, since that level of trust is there already, but BE AWARE.
I personally use KeePass, but any of the major password managers available are fine. I know that KeePass has an iDevice app with Drobox support, and it's likely that others do as well. (Password Safe does not.)
EDIT: There is related discussion at IT Security.