Do you mean his family pre-marriage or post marriage?
If pre-marriage, there are only 2 ways of getting that info - either by buying a copy of his birth cert or by looking him up on the 1911 census which is strictly pay per view
There is a free index and I have shown some instructions which may help you
USING THE FREE 1911 INDEX TO DETERMINE THE CORRECT HOUSEHOLDhttp://www.1911census.co.uk/search/tnaform.aspxOnce you find a possible match - make a note of the county and district in which the person was living
Return to the index and in PERSONAL DETAILS - just put the surname of the family - nothing else
In LOCATION - Select the county and below it - type in the district
In OTHER MEMBERS OF THE HOUSEHOLD - show the full name of the person you have found on the index
Click SEARCH
You will have to buy credits to view the full entry - the above instructions will only help to possibly show others of the same name in the same household
If you mean post marriage - you can search freebmd for Griffiths births with mothers maiden name Bate which will give you details of his family
Because the marriage was 1927, any children could still be living so we cannot post details here