Bumhouse...is this your first dog? It's unlikely that a 15 week old pup is aggressive. I am guessing that you're confusing normal puppy behavior with aggression. Puppies don't come already knowing how to live with human rules. That's the way puppies play. They greet eachother by jumping up. So, you don't want to be harsh but you can show him the human way of greeting, he sits first.
What are your reactions to the pup when he is acting wild? If he continues to get any kind of attention when he bites and jumps, this will reinforce this behavior. All playtime needs to end immediately and no further attention of any kind. If he knows sit, then when you see him have the intent of jumping or biting, ask him to sit and reward for that. Give alterantive chew things to bite on.
Teach him that only sitting nicely will get him attention and even a treat. But by jumping up and nipping...all fun will stop and you'll turn your back away.
Everyone in the family must do the same and it must be very consistant....never once wavering from this. He will continue to try to get a payoff by these antics because they have worked for him up to now. You need to convince him that that behavior will not work to get him anything he likes. Dogs do what works so remove any possibility of a payoff for this behavior. Preventing or intercepting him from jumping or biting is better than waiting until he already does it. Be ready to give him an incompatible alternative....something he can't do and jump at the same time, such as sit or something he is allowed to chew on and praise him when he is chewing on his own stuff.
Is he getting plenty of romping outside and enough exercise? Get him a little tired out a few times a day. Run through his skills several times a day for a very short period. Even here and there, ask for a sit or down. Let him learn what behavior gets him the good stuff and what doesn't. Stay with it. Most puppies who seem out of control aren't getting enough exercise (although you don't want to do more repetitive stuff than his bones can handle while they're growing) But plenty of free running in the yard is fine.
So, mind and body work, showing him what you do want and reinforcing it with something he reeeeeeeeellly loves....distracting from behaviors you don't want, giving alternatives, reinforcing those. Ignoring behaviors where the payoff is your attention...ie: jumping up, nipping. If the biting is really bad, some dogs respond to a loud yelp, as if it really hurts, then ignore him, but give him a chew toy to teeth on. Show him what he CAN chew on.
Be sure to let him know that you and your family members control his resources....the things he likes, needs or wants; food, toys, attention, getting his collar on, opening the door for him etc. He needs to earn a lot of those things by sitting first or some other trick.
If you're consistant and train him with decisiveness without harshness....consistancy and gentleness, show him what you mean, reward....he'll outgrow this. Make him trust you explicitly and he'll look up to you even more and decide that paying attention and trying to learn your ways is the only way to fly.