i think there is not, as far as we were aware, it is left to the descretion of the company that your husband works for. some are kind enough to offer a week, my husband's 2 days... which they still called him for meetings!!!
It really depends on the company. Most of the local Chinese firms don't have such leave whereas some foreign companies may have such offers. My husband works in a US investment bank and can enjoy 10 days leave.
My oldest was born on Easter Sunday, so my husband had that day and Easter Monday off. He had to take a day of annual leave the day we left the hospital.
My second was born on a Wednesday. My husband had to take 2 days of his annual leave to be with me at the birth and the next day, plus a half-day the day that we left.