Connect Docker container to both host and internal bridge network
Docker does not allow to connect a container to the host network and any other Docker bridge network at the same time. I will try to illustrate the reason with an example:


Let us think of a container C1. Hypothetically, C1 would be connected to the host network (--net=host) and a Docker bridge network Br1 (--net=Br1).
A second container, let us say C2, is connected to Br1.


With the above setup, my guess is that the host network is visible from C2, and I suppose this is the reason why Docker automatically prevents us from unintentionally exposing the host network to non-host-specified containers.

That being said, if we have a set of containers, and we want all of them to be interconnected, with just a single container having access to the host network, my approach would be:


[C2,...,CN] are connected to a user-defined Docker bridge Br1 (--net=Br1)
C1 is connected to the host network (--net=host)
C1 exposes a port in order to be accessible from the rest of containers


EDIT: We would still have to adapt iptables policies in such a way that C1 can be reached from the rest of containers (see https://docs.docker.com/network/iptables/)