Domain Controller with two Network adapter

I have a Windows Server 2012 R2 with Domain Controller and DNS server role and it have two net adapter.

Even the DNS is not listening on the public adapter and the adapter have no registration of DNS setup, when I use Get-NetConnectionProfile to check the profile it returns:

Name             : mydomain.com
InterfaceAlias   : Public
InterfaceIndex   : 13
NetworkCategory  : DomainAuthenticated
IPv4Connectivity : Internet
IPv6Connectivity : LocalNetwork

Name             : mydomain.com
InterfaceAlias   : Private
InterfaceIndex   : 14
NetworkCategory  : DomainAuthenticated
IPv4Connectivity : Internet
IPv6Connectivity : LocalNetwork

The problem is that I need to set the interface index 13 to NetworkCategory Public and not DomainAuthenticated.

I have already tried to Google it but no way to find a solution.

Giuseppe