You will need to speak with your current insurance company to find out if they will allow you to add your boyfriend and his car onto your policy. Since you are both living in the same household many insurance companies generally would allow for both vehicles to be listed on one policy.
In general, it should be less expensive if you and your boyfriend to get a multi-car policy for your household provided that your current insurance carrier will allow for both of your vehicles to be on the same policy without you two being related or married. If they do not you may want to shop around for an auto insurance specialist that will allow this.
If you find an insurance company that finds this type of policy acceptable (one including you and your boyfriend), then typically a multi-car insurance policy will be cheaper than individuals that have separate policies on their own. A multi-vehicle or multi-driver discount may apply so ask the insurance carrier and also ask if there are any other discounts that you or your boyfriend may receive.