Fluffeh it's hard to imagine now, but - once you've recovered a bit from the CS - you will almost certainly feel absolutely fine about being left with the baby while your DH pops out for a short while.
Being with your own baby is totally different from other people's. When I was pregnant the first time, a friend visited with a 6 week old. I was so impressed with DP, he was so good at holding the baby. I on the other hand found it really awkward and I was scared I'd drop her or hold her wrong, and I thought "oh my goodness, I'm going to be really bad at this when my baby comes!"
But when DS was born, holding him just came naturally! My mum actually asked me how to hold him when he was 2 days old! You'd think, with experience of bringing up two DDs and of holding countless other babies, my mum would be teaching me. But in reality, she'd forgotten as it'd been so long, and in just a day or so I had become more of an expert on how to hold DS than her.
The teacher in this scenario was not my mum, or me even, but baby DS. Babies teach you how to be a mother. It's partly that they're not going anywhere, they are there, and you just have to get on with it, so you learn quickly. They tell you if you're doing it wrong! But it's more than that, instinct is a very powerful thing.
You're absolutely right that with a baby, there are suddenly lots of logistical challenges to deal with. How to go shopping in the supermarket with a baby in tow, for example? I went in with the buggy the first time, and balanced lots of food on it, I must have looked like I was shoplifting! It worked, but wasn't ideal! The correct answer, I later discovered is you put them in a baby seat on a special trolley. I'd never noticed them! Or simple things, like how to have a shower when it's just you and the baby? (For me, the answer was to put DS in a bouncy chair in the bathroom with me, and coo at him while showering. I forget how old he was when we started doing this).
You'll be fine I promise. It's great that you're able to discuss your fears with your DH and he's being so supportive. However I wish I had a crystal ball to show you you and your baby together, you will be an expert mum in no time!