The idea of Ajahn Brahm sounds strange to me. I imagine there is only one type of Satipatthana, which means to "establish mindfulness". What this means is whatever body, feelings, mental states or Truth/Reality is/are experienced; the mind 'remembers' ('sati') to not have covetousness & distress towards those bodies, feelings, mental states or Truth/Reality.
Jhana (Appanā Samādhi) is merely a higher level of feelings (2nd satipatthana) and mind (3rd satipattana) than experienced with the lower Neighborhood Concentration (Upacara Samadhi) of Anapanasati. Therefore, mindfulness is established towards jhana the same as towards any other experience, as explained in many suttas, such as below:
Whatever qualities there are in the first jhana... he remained unattracted & unrepelled with regard to those qualities, independent,
detached, released, dissociated, with an awareness rid of barriers.