Comment 3 for bug 1622730

So, after a while tried it again and I finally managed to get the headphone jack working:

1) Update to grub2 if this has not yet been done.

2) Set the following acpi kernel parameter in /etc/default/grub

GRUB_CMDLINE_LINUX="uveau.modeset=0 acpi_enforce_resources=lax"

3) update-grub

4) Reboot

5) After suspending, run init-headphone to reactivate the headphones.

You can automate the headphone reactivation by adding the script /lib/systemd/system-sleep/init-headphone with content:

#!/bin/sh

if [ ! -x /usr/sbin/init-headphone ]; then
    exit 0
fi

case $1 in
     resume|thaw|post)
        /usr/sbin/init-headphone
        ;;
esac

This is similar to old workarounds found elsewhere on the web, but with xenial /lib/systemd/system-sleep/ has superseded by /etc/pm/sleep.d/ and the case "post" has to be added.