Burnhal's answer is only partly true.
A CRB check at 'standard' level will only show information about yourself. This will be restricted to convictions and cautions.
A CRB check at 'enhanced' level can also show any additional information that a senior police officer (or other relevant body, such as Social Services or the Department for Children, Schools and Families) deems relevant. This can include unproved allegations against you as well as offences committed by (and unproved allegations against) anyone you regularly associate with.
The police and CRB, together with relevant agencies are under pressure to ensure that all relevant information is passed on. This follows the Soham murders. Understandably, the authorities believe that the past unproved allegations against Ian Huntley should have appeared both on his own CRB check and on Maxine Carr's as well.
I know of a teacher who has a family member who has been convicted of downloading child porn. This offence appears on her enhanced CRB check. Similarly, there's been a post on AB from someone who found a partner's offence mentioned on her enhanced check.
Your partner's offence will not show up on a standard level CRB check. It will show up on an enhanced level check if someone 'in authority' is aware of it and deems it relevant.
Chris