What you are trying to achieve can be accomplished by employing "Split tunneling".
You may need to configure a split tunnelling policy on your VPN appliance or your VPN service for this.
The process involves defining ACL`s(Access Control Lists).
For an example, If you want all the internet traffic to go through your Physical Network Adapter(Rather than the Virtual Adapter which is used for VPN), Define an ACL which does allow any internet traffic through the Virtual Adapter.
Ex : Consider that you have a mail server named mail.xyz.com in the intranet which needs t0 be accessed through the VPN. Create an "ALLOW" policy for this host.
When the computer tries to reach any other resources through the tunnel will be denied access and it will fallback to physical adapter.