Zero hour contract, can dh get uc for paternity leave?

[finallysummer]

Dh is on zero hours but he works a lot of hours about 50 a week and we get a UC top up because we have small children.
I'm also pregnant but dh isn't entitled to paternity leave through his employment so would he have to take annual leave or is there a statutory paternity he could apply for?

Have a look on gov.uk at Statutory Paternity Pay x