Introducing new puppy to my 3 year old dog?

Hello,

I recently brought home a 4 month old mini labradoodle. I have a lab/boston terrier mix already, and I am working on getting him to warm up to the puppy. I am able to walk them side by side consistently, and I can let them off leash at the park. However, I still do have to keep an eye on my older dog because sometimes he snaps when they come face to face after they chase each other. He is completely fine until she is close to his face, or when she jumps on him (which she tries to do a lot!). He naturally retaliates by growling and snapping at her. I don't think he has intention to actually bite her, but I always intervene when he does that. For the most part, I keep them separated in the home. It's been a little over a week since I brought her home. Any advice? Should I allow him to teach her what's not acceptable by snapping, growling, etc? Keeping them separated is frustrating because if I do anything with one dog, the other gets jealous!