Your partner is right. Four weeks isn’t always as long as a month. My baby was born on the 21st so she goes up a month on the 21st of each month.
Age in months and age in weeks are two totally different calculations! And don't mix well. Every 4th your baby will be a month older. Every Monday your baby will be a week older. But they are separate units of measurement.
So in terms of weeks it would be today but for month it would be 4th as your hubby said. Weeks and months are diff and you’d calculate a month based on birth date like we do for our bdays. My son was born on 30th October a Wednesday. So 4 weeks was Weds 27th but he was a month old form his birth date on 30th Nov. I’ll be doing the monthly pics on 30th each month and then he’ll be 12 months/1 year on 30th October 2025