I'm afraid that Jitterbit just extends dataloader functionality. You have to describe how child is related to parent. That's why you are using three operations.
But you can reduce it to two operations by implementing external Id in you parent object. Just define in csv external Id for parent and provide it for correspondent children records.
How do I use an External ID to import related records?
You will get rid of pulling and populating Ids.
Another way is to utilize SObject Tree
But it will require some programming. I'd prefer to create win service, which runs python. And in python you can do implement your extract, import etc.