Backup of a Debian machine to an Apple Time Capsule
In AirPort Utility, turn off the backup feature, turn off disk encryption, and turn on disk sharing with a password. Now you can connect to the disk over the network using the AFP protocol.

In most graphical file explorers you can now connect to the disk using the address afp://&lt;ip-address-of-airport&gt;. To easily configure scheduled backups to the device, you can check out Déjà Dup (known as simply “Backup” in Ubuntu).

You cannot backuo your Macs using Time Machine and your Linux machine to the same device. The two setups are incompatible as Time Machine requires proprietary extension to AFP. I would recommend you get a cheap Raspberry Pi and a two-terabyte power-over-USB-external-disk to host your Linux backup needs. (Install openssh and ufw, and you’re basically done setting up a simplistic firewalled backup device on the cheap.)