This can also be done using RedGate SQL Compare command line. You can create a batch that takes a snapshot of the databases that you are interested in and then compare against the prior months snapshot.

SQL Compare will also allow you to create a separate HTML file for each compared datatabase. This would not only indicate the objects that have changed, but also how they changed. We have been running this for several years.

Since this does not rely on triggers you do not have to be concerned with what occurs during times that the trigger is disabled.