Set up wired ethernet LAN to coexist with wireless WAN using NetworkManager

I have two network interfaces on a client PC, one wired, one wireless. The wired is connected directly to a server PC running DHCP, which gives the client PC a 10.0... address. The client PC also connects to a wireless router, which gives it a 192.168... address. This was all set up and detected automatically by NetworkManager. I am able to ping the server PC and wireless router. The problem is I want to use the wired connection as a LAN only, and the wireless for WAN access to the wider Internet. But NetworkManager thinks the opposite, and tries to use the LAN to go to the outside Internet. If I unplug the cable it correctly uses wireless. But I'd like to have them both connected at the same time. I'm running Debian unstable if that matters. Is there some way to configure this?