Miley Cyrus does write or at least co-writes many of her songs on her most recent albums (according to this). In the past her songs were written by others, including her dad a few times, and staff writers quite often. For example, the theme song for Hannah Montana is “The Best of Both Worlds” written by Matthew Gerrard and Robbie Nevil.
In terms of the Jonas Brothers, if you go to Wikipedia you will find a list of the Jonas Brothers’ songs with the writers. Many of the songs are indeed credited to the Jonas Brothers themselves, a few are credited to the Jonas Brothers and Miley Cyrus, many show shared credit between the Jonas Brothers and other writers, and some are written by someone else.
However, the problem with song credits is that they do not show who contributed what or how much. For example, while the Beatles existed as a group all songs written by John Lennon and Paul McCartney, or John Lennon by himself, or Paul McCartney by himself, were credited to Lennon-McCartney.
I think it is safe to say that both Miley Cyrus and the Jonas Brothers have written some of their own songs. Also that, as they all mature they will most likely write more and more of their own material.