What you want is referred to as split tunnel. Split tunnel allows you the vpn while keeping open the internet connection to the outside.
Reason most vpn products don't do split tunneling is it compromises the security of the vpn. It could allow a hacker in control of your pc [unbeknown to you] access to what is on the other side of the vpn.
Solution would be to find vpn software that allows split tunneling though if you connected to my work that way you would be fired for compromising the company's security.
The information on Computing.Net is the opinions of its users. Such
opinions may not be accurate and they are to be used at your own risk.
Computing.Net cannot verify the validity of the statements made on this
site. Computing.Net and Purch hereby disclaim all responsibility
and liability for the content of Computing.Net and its accuracy.