H.G.
Your husband needs to try (so hard!!!) to not take this personally. It's such a normal response from a toddler! But very painful for dad. You can help tremendously, too. Talk positively about your husband all the time to your son, and basically MAKE him spend time with his daddy! When he pushes dad away, don't give in. In a chipper voice, say, "Daddy's helping you, I need to go ____________." Then walk out of the room. Even if he screams and tantrums. (He will!)
Keep doing this! Also, your husband should take him out for dad and son outings a ton. Breakfast at a diner, to a museum, etc.
Finally, create a routine now that incorporates a lot of daddy into it. This will help you so much when the new baby is here! If it's always daddy who comes and gets him in the morning, for example. And if it's always daddy who gives him a bath. Those types of things will keep your son understanding what to expect, as well as give you the time you need with your newborn!
Your son is scared and insecure about this new baby. That's totally understandable! So he wants to suction himself to your side and never leave. :) But he'll figure it out, with a little help. And your husband has to take the high road here, even though his heart is a bit bruised.