I think the answer you're looking for is [here][1].

Blatantly plariarised:

You can add the following line to `/etc/dhcp/dhclient.conf`:

    prepend domain-name-servers <working DNS IP(s) here>;

This adds the DNS IP address(es) you specify _before_ that/those provided by the DHCP.
If you would like to add it/them after the address(es) provided by the DHCP, just use

    append domain-name-servers <working DNS IP(s) here>;

If, instead you would like to ignore the DNS address(es) provided by the DHCP altogether, use

    supersede domain-name-servers <working DNS IP(s) here>;


  [1]: http://unix.stackexchange.com/questions/146463/specifying-dns-settings-to-override-those-of-dhcp