Open Edit → Virtual Network Editor, and click Change Settings. Set VMnet0 to Bridged, and choose to bridge it to a specific network adapter (not Automatic), then click Add Network, and bridge that one to the other network adapter. You can also rename this network (for some reason, you can't rename VMnet0). Close Virtual Network Editor by clicking OK.
In the VM Settings, add two network adapters, choose Custom for both of them, and assign VMnet0 to the first one, and whatever you named your second one to the other adapter. Your VM now has two network cards, each connected to a different network card on your host.