Becky is right...without specific examples it is hard to say whether or not the behavior is normal...
I must say that I have 2 boys (both adopted at infancy) and 3 was definately the toughest age...they want independence, and want what the want when they want it, and if they didn't get it, well, let's just say that a 3 year old can bring you to your knees...
Consistency is the key...One of the behaviors that my youngest had at 3 was throwing things...Didn't matter if he was happy, sad, ticked, whatever. He threw everything...We were consistent, and the behavior stopped...but let me tell ya - it took a year. Not an easy fix.
What kind of behaviors is your child exhibiting?
ETA: I just saw your other thread...I read that your son has only been in your home for a month, and that he has special needs...You said "when he won't do what he needs to to get out of trouble and just digs a whole deeper". I'm sure you probably meant this different than it sounds (it's hard to really convey our true intent over the web, isn't it?) but a 3 year old doesn't have the cognative skills necessary to to counteract behavior in order to get themselves out of trouble...That's just not within their realm of understanding...
Your one example is that your FS jumped on your stomach...That sounds like typical 3 yr old behavior to me...Now unless something lead up to this, it's hard to tell where his frame of mind was...and I see that your DH was angry because he's very "protective" of you...and that's very commendable. But really, a 3 year old, especially one with special needs, doesn't understand the "extra" consequences of jumping on a person with medical issues, so although it is normal to be upset at the behavior, it is important to distinguish being upset at the behavior, and being angry at the young child because you are feeling protective over another adult...Does this make any sense?
What other situations have there been? And are there any "triggers" that lead up to these "issues" that your FS has? It may be helpful to try to pinpoint these triggers, and when you see them coming, take appropriate actions to redirect your FS...And remember - this is all so new...with time and consistency, things can change...but remember - he's in a new environment, with new parents and new rules, he has special needs, and it is the holidays, which makes everything all the more intense...