I found the solution. in /etc/network/interfaces, the dns-nameservers line has to be on interface lan0 (the internal network).
In addition, lan0 must be defined before eth0 (the external network), otherwise resolvconf will add three ipv6 nameservers and no ipv4 nameservers.
# armbian-config created
source /etc/network/interfaces.d/*
# Local loopback
auto lo
iface lo inet loopback
dns-nameservers 127.0.0.1
# Interface lan0 -must be before eth0, because eth0 generates too many dns-nameservers
auto lan0
allow-hotplug lan0
iface lan0 inet static
address 192.168.0.15
netmask 255.255.255.0
dns-nameservers 127.0.0.1
# Interface eth0
auto eth0
allow-hotplug eth0
iface eth0 inet static
address 192.168.100.10
netmask 255.255.255.0
gateway 192.168.100.1
