A user passed on the following information to me so that Handcent would play nice with Enhanced SMS & Caller ID+:
  • Open Handcent SMS
  • Click on the Menu and go to Settings
  • Under Application Setting there is a setting called Default Messaging Application.
    The description for this setting is:

'Set Handcent as default messaging application and entirely disable the stock and and other third-party application for SMS or MMS' Options are Disable, SMS, MMS, & All(SMS & MMS).

Set this option to Disable, which I presume disables this feature and allows other applications to receive SMS/MMS notifications.

Some newer versions of Handcent also have the ability for you to give Handcent a lower priority. If you enable this option, other 3rd party apps, like Enhanced SMS & Caller ID can receive incoming messages before Handcent does.