What do you mean? You share a house with another person? Anyway, if you have different name with you roommate, I think you should have your account.
But i think its better to ask google, cos the System used by both may be the same. Hence, IP same & Accounts problems may arise.
I think it should be ok. I use cable internet here... which has around 1000 other subscribers in this area. The same IP address goes out from all the people. May be there are other adsense users also around me, and the same IP used for them and me. But still.... the house address would be different anyway...