Bridge specific VM to a physical adapter in vSphere

I have a server with 4 physical network adapters which is currently running VSphere 5.

On top of the hypervisor, I have 3 OS; 2 Linux and 1 Windows. Each of the Linux has 2 virtual network adapters. The Windows only have 1 virtual adapter.

The objective I'm trying to achieve is

Linux 1
Virtual adapter 1 -> eth1
Virtual adapter 2 -> vmnet

Linux 2
Virtual adapter 1 -> eth2
Virtual adapter 2 -> vmnet

Windows
Virtual adapter 1 -> vmnet

The vmnet is a virtual network whereby the Windows can manage (SSH) Linux 1 and Linux 2.

For that, I have created 3 vSwitch. vSwitch 1 and vSwitch 2 is bridged to vmnic1 and vmnic2 respectively. vSwitch 3 is not connected to any physical adapter. Each of Linux Virtual Adapter 1 will connect to vSwitch 1 and 2 respectively while the remaining Linux virtual adapter and the Windows will connect to vSwitch 3.

Is my vSphere network setup and understanding correct here? If my explanation is confusing, here is my diagram:

Thanks