I switched from unstable 4.1.2545 to stable 4.2 on Ubuntu 16.04 yesterday.
Following the download wiki I changed the line
deb https://dl.bintray.com/tvheadend/deb xenial unstable
to
deb https://dl.bintray.com/tvheadend/deb xenial stable-4.2
This worked for me without any problems, but keep in mind, that I was already using the latest unstable version (4.1.2545).
In your case you would probably have to change the line
deb https://dl.bintray.com/tvheadend/deb jessie unstable
to
deb https://dl.bintray.com/tvheadend/deb jessie stable-4.2
for the stable 4.2 builds, or:
deb https://dl.bintray.com/tvheadend/deb jessie release-4.2
for the release 4.2 builds.
After that I just ran "sudo apt update" and "sudo apt upgrade" to update my TVheadend server on Ubuntu 16.04.
It automatically started without any further configuration needed.