Split Tunnel and Cisco AnyConnect

First understand that the reason your network admins have disallowed split tunneling is because it potentially allows any malicious person/code to circumvent the security measures that have been implemented by accessing the network via your computer. Believe me I know not having a split tunnel is annoying, but ask your self is it worth the risk?

Now that warnings are out of the way I can tell you Cisco AnyConnect prevents a split tunnel by temporarily re-writing the routing table of the host computer. Use route print before you start AnyConnect and use it again after to see the differences. You can write a script to adjust the routing table and run it after you start AnyConnect. An easier solution that probably doesn't violate your networks usage policy is simply using a VM with AnyConnect. Your host's NIC doesn't get locked down and you don't break any rules... best of both worlds.