Good posts Omnia and porca. We do have 3 DC, third unplanned. I did want a third, DH didn't, but contraceptive did not do its job properly. I love having three, so completely sympathise, but there are downsides and I think these are what you will have to focus on.
You also have to focus on the fact that you have two healthy DC already. I was very worried throughout my third pregnancy about the health of the baby. I didn't have amnio as I could not have made a decision if the result had been that there was something wrong with the baby.
If you have three DC, one is quite often left out (doesn't always happen, but it does happen).
Getting babysitters for three is much harder than for two.
YOu may need a different car.
If you've only got a three bedroomed house, two DC will have to share.
DH had the snip while I was still pregnant with number 3 so that is all we have. Perhaps you could suggest that to your DH then the decision will be taken away from you and that might help you.
Having said all the above, I love having three DC and now feel the family is complete. Actually, I would have loved to have four, but for various medical reasons, couldn't.
Good luck, OP.