I can totally understand your frustration. My DH was at that point for different reasons after we'd had two, I had major complications with the 2nd birth, which I'll likely never fully recover from.
I never really stopped wanting a 3rd but eventually I did get to the point where I could see his logic and as my kids moved beyond the baby and toddler stage I did start to feel it would be a huge upheaval to go back to having a baby, I even made an appointment to see my doctor to talk about longer term contraception, possibly even a tubal. However when I went in I lost my nerve and just dealt with some other issues I'd gone in for. It turned out that I was already pregnant at that stage.
We'd been using a diaphragm or condoms, so the most likely failure was the diaphragm. I had good reasons for choosing a diaphragm, I don't do well with hormonal stuff, neither of us like condoms, already had very painful periods, so didn't want an IUD etc. but deep down, when we chose that I was glad that it was less reliable than other methods, though I still tried to observe my fertile signs and avoid that time of the month.
Our DD is 6 months now, we love her to bits, DH understood and accepted the risks of our chosen contraception, but the combination of our emotions through the pregnancy was very hard, he was initally thrilled, whilst I was frightened. I had PPD after our first, but not our 2nd, so I was definitely aware of the possibility as it turned out, I actually became depressed in the pregnancy and have been having a very hard time and not responding well to treatment. Even in the depths of despair, I still think I look back a year from now, or 5 years from now and be thrilled about our oopsy.
You don't say how old your DS is, but you've only just got to the point of wanting another baby, you can't expect your DH to get there at the same time, in 6 months time he may feel very differently. One thing that really influenced us in having a 2nd after PPD with our 1st was me talking about how PPD was something that I didn't expect and that I wanted to move beyond it, that I didn't want it to be something that shaped our lives forever and that we could choose to be fearful and not extend our family or we could step back and see the bigger picture and that 5 or 10 years down the line even a 2nd bout of PPD would be a thing of the past.