From an INetwork instance, you can get the list of connections (INetworkConnections instances) using the GetNetworkConnections method.

Then, using the INetworkConnection::GetAdapterId method, you can get a Guid that represent the adapter Id. The adapter Id in fact matches the NetworkInterface.Id Property (it's a string, but you can convert it to a Guid).

Here is a sample console app that dumps all network and their connections, and interface properties (type, name, etc.):

class Program
{
    static void Main(string[] args)
    {
        var mgr = new NetworkListManager();
        foreach (INetwork network in mgr.GetNetworks(NLM_ENUM_NETWORK.NLM_ENUM_NETWORK_ALL))
        {
            Console.WriteLine("Network: " + network.GetName());
            foreach (INetworkConnection conn in network.GetNetworkConnections())
            {
                Console.WriteLine(" Adapter Id:  " + conn.GetAdapterId());
                var ni = NetworkInterface.GetAllNetworkInterfaces().FirstOrDefault(i => new Guid(i.Id) == conn.GetAdapterId());
                Console.WriteLine(" Interface: " + ni.Name);
                Console.WriteLine(" Type: " + ni.NetworkInterfaceType);
            }
        }
    }
}