Comodo Secure DNS behind an Active Directory domain

Please see my scenario: I’m using a stand-alone computer (i.e., not joined to a domain) inside a network managed by an Active Directory domain. Even though my computer is not a domain member, it uses DNS servers provided by the corporate network DHCP, which happen to be the AD DNS servers. When I need access to some shared resources in that network, I authenticate myself on demand, and everything gets fine.

But a lot of things go wrong when I change my DNS to Comodo servers. Several internal addresses does not resolve anymore, local, Windows machines can’t be traced anymore (by tracert command), etc.

My thought: is it possible to set up Comodo DNS to resolve internet addresses and keep intranet addresses to be resolved by AD DNS server? Is there any other workaround to this problem? I’d like to keep the safety Comodo DNS offer to me when in the “wild”…

Thanks in advance.