Generally, they can search anyplace that the parolee has access to. If you are in a house or car, then anywhere in that house or car that the parolee has access to can generally be subject to a search. This will generally NOT include a search of your person, but if your purse or other bag was readily accessible by the parolee, those items may be subject to search.
Bottom line is if you do not want to risk a search, then don't live or travel with a parolee. Keep in mind that if the police or parole agents are not satisfied, it may be possible to revoke his parole. So, if you are obstinate, HE may pay the price for your obstinance.