In the book Birkenhead At War, by Ian and Marilyn Boumphrey, the air raid on 12/13 March 1941 is recorded as the worst inflicted on Birkenhead, with 288 people killed and 275 seriously injured. A large area of the town and its suburbs were blitzed.
The Civilian Roll of Honour in the book includes -
Michael Cavanagh, age 41, of 70 Beckwith Street, husband of Elizabeth Cavanagh. Killed March 12 at Beckwith Street.
Their son William Thomas Cavanagh, same address, age 15. Injured March 12, died at General Hospital.
It's worth noting when researching the Blitz that wartime newspapers were heavily censored and details of casualties and locations would probably not be given at the time.
It may instead be useful to check newspapers from subsequent anniversaries, when they may have published retrospective stories with more details. For instance, in 1971, the Birkenhead News
did a series of features marking the 30th anniversary of the Blitz, with lots of interviews of those who had lived through it and stories of the destruction.