Upon clearing House of the Dead 3, you unlock the ability to play on Very Easy or Very Hard, along with the ability to use 5 lives and 9 continues.
House of the Dead 3 Extreme Mode
In order to unlock the one-player only extreme mode for House of the Dead 3, you need to beat both House of the Dead 2 and House of the Dead 3. Extreme mode requires you to hit weak points to kill enemies and allows the use of a blocking attack.
HotD 2 Cleared Unlockables
Upon clearing House of the Dead 2, you unlock the ability to play on Very Easy and Very Hard, along with the ability to use 5 lives and 9 continues.