'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.