Views on parenting is causing problems

I’m at a loss with my husband and our parenting views together. We’ve spoken so many times about it, but it always seems to be the root of our arguments these days...and our daughter is only TWO. We have another one on the way this fall, as well. Before we had kids we were aligned. He was raised by his dad and his dad was very tough on him. My parents were always strict, sometimes too strict. So we said we’d always be more understanding and patient with our children. I’m in the education field, so I know how important patience is (within limits). I am certainly not a pushover and he definitely isn’t, but when my daughter is a having a tantrum (which is normal at this age), I’m not very reactive. What will that do for her as she’s screaming on the floor throwing herself around? Nothing. I’m more of a reflector. Of course, if she’s hitting or throwing things, it’s a non-negotiable time out because she knows that is not okay. My husband thinks we’re too lenient and she “needs punishment that she’ll remember.” Like what?! She’s TWO. We always talk over how we handle things and he always agrees he should be more patient...and then she has a freak out and he’s back to telling me how wrong we’re parenting. I love him so much and he is an amazing father, but I honestly can’t see myself parenting like this for the rest of my life. It’s draining!! I don’t know if I’m just venting or need advice on how to approach it differently. How do you and your SO see eye to eye on parenting?