Scott B,
Currently there are no means to sync 2 or more phones together. When I say sync, I mean you add a bill and your wife would see it added to her phone or vice versa.
The easiest solution to this problem would be for one person to have the app and be responsible for maintaining bills. Sync the bills to a google calendar that is shared and have that calendar visible on your wife's phone. She'll be able to see updates, etc to the bills that you make. To further expand on this, if she changes the contents of the calendar event it will not change the information on your phone. Changes are only driven from the phone.
-Scott