Welcome to parenthood and the world of 3 year olds. The issue here is that you're trying to suppress a child's natural exuberance and noise levels, and I sincerely doubt that he's any noisier than any other normal 3 year old. What makes him seem super noisy is the fact that your husband wants to sleep in the morning (I'm guessing with relative quiet). You're also feeling stressed because it's your responsibility to keep your son "behaved enough" to stay quiet and out of trouble when really he's behaving normally.
It's time to stop saying "no" and being so restrictive at a time when your son's energy is at its highest. He shouldn't be punished for normal behavior, normal playing, because you're stressed out and not getting a break.
Get your husband some soft foam ear plugs. They can be found at the pharmacy and in the manly color of blue so that your husband can be comfortable wearing them and block out most household noise while the bedroom door is closed and he sleeps.
I would also set a schedule that's more fair so that your husband isn't sleeping all day. He ought to get up a couple of hours sooner than he is now, at least, so that he can help you with errands, household chores, and spending time together as a family. It would also give you time to pamper yourself even if it's only to run to Dunkin Donuts and grab a muffin and a coffee to eat while you read a couple of chapters of a book.
See if you can start planning play dates. Check with your local elementary schools and see if they have a Family Resource Center or equivalent that hosts frequent play groups. Often times if a town has several elementary schools, one of the schools will take turns hosting a play group each day of the week. So if a town has three elementary schools, there might be three play groups each week. Check and see if there are MOPS groups in your town. Sometimes they're hosted in a church center or basement but they're not churchy. They're just Moms of Preschoolers... moms get together to meet and chat while their children can play and are watched in another area.
If you have family or friends in the area, start taking some advantage of any offers of help. ASK for help. It's okay to ask for help.
With your son, try positive language as much as possible rather than negative speech. "No" doesn't work as well as "I like it better when you ____" or "Let's try this way instead." Praise for positive behaviors works wonders as well. "I'm so sad that you {unwanted behavior}, but I was very proud of you for {good behavior}. Let's {do good behavior} again." Even saying, "When you {unwanted behavior} it hurts my feelings. You need to {desired behavior} instead." Try to eliminate "no" as much as you can and give him credit for understanding language better than he's able to express it.
Part of the purpose of this is to make your son learn to be accountable for his actions by making good choices. "You can choose A or B. If you do A, then will happen. If you choose B, then this will happen. You may not like what Mommy will do if you choose B, but it's your choice." Follow through, and make sure that ANY consequence you choose to threaten with is something that you are prepared fully to follow through on until the end. Avoid phrases like "always" and "never."
Don't underestimate natural consequences. For instance, if he's climbing where he shouldn't and he's about to pull something down onto himself but you know it won't break or cause him to require stitches, then give him a warning that if he continues with the undesired behavior he's going to cause _____ to happen and you would like him to stop. Warn him that if it does happen, he'll be responsible for cleaning it up even if he gets hurt. Then when it does happen, and you make him clean it up, but you don't make a big deal about his wails of pain and fury, he'll have learned a lesson.