Insurance company guidelines and rating systems differ so you will need to check with your insurance provider to find out if your rates will be affected by your son's DUI. While he remains on your policy it is likely that his DUI will cause your rates, as the policyholder, to rise since alcohol offenses are normally taken seriously by an insurance carrier.
As you are aware the driving record of any licensed driver on a policy or in a household can have an impact on the insurance premiums as well as the insurance company's decision to insure the vehicle. Certain infractions may cause an insurance carrier to turn you or the policyholder down for insurance coverage or to pay high-risk premiums.
You will need to find out what it will take to remove or exclude your son from your policy by speaking to your insurance agent. If your son takes out his own car insurance policy you will probably be required to show proof of his policy to your insurer in order for them to remove him as a driver from your policy.
If your rates rise then it may be time to start shopping around for new insurance coverage. Get a quote here from an auto insurance specialist.