I'm using Try...Catch to handle errors that occure during the transaction. But it still rolls back.

This is the correct behavior if an operation with database is performed and an exception is catched within Try, it still causes a rollback.
You will see "Errors have already occurred in this transaction!" message as for not catched exception. At the same time if non database-related exception occured, it can be catched and will not cause a rollback.