If you don't have "managed=true" in the "[ifupdown]" section of "/etc/NetworkManager/NetworkManager.conf"?
If you don't, NM will ignore the NIC that you've defined and set up in "/etc/network/interfaces".
How are you setting the DNS servers in "/etc/network/interfaces"? The only way that you can do so (using "dns-nameservers ...") is if you have resolvconf running and "/etc/resolv.conf" is a symlink to "/run/resolvconf/resolv.conf".
(If you don't use "dns-nameservers ...", you have to use "/etc/resolvconf/resolv.conf.d/{head,base,tail}" to set the nameservers in "/etc/resolv.conf", unless you want to use those that you get via dhcp.)