In marriage, can one party legally open the parcel (such as Amazon delivery) to the spouse? (Assuming it is delivered to a house owned by the couple.)
This website seems to say for mail answer is no. But how about parcels/packages?
It is a crime to remove mail from an authorized mail depository, and an official mail box is (by definition) an authorized mail depository. Not every object used to hold mail is an authorized mail depository. It is also illegal for Amazon etc. to deliver to official mail boxes. Parcels can be delivered by USPS to official mailboxes, bringing such parcels under the purview of 18 USC 1708. Your front porch is not an official mail depository, and it is not a crime to remove a parcel dropped somewhere unofficial on your property. The pertinent distinction is not about "letters vs. packages", it is "Federal mail of any kind in an official depository".
It can easily be the subject of a lawsuit to trespass on the property of another person, in every state of the US. If A trespasses on B's property, B can sue A and recover damages. B would have to prove that the item was their property (A could defend against the claim by proving that it was A's actual property or that it was joint property. The theory that spouses have equal rights to items acquired during a marriage is not completely wrong in certain states, for example Washington, but not Ohio). Of course if it is reasonable to believe that the package contains a dangerous substance then A's decision to inspect the contents could nullify B's claimed outrage over the trespass, and A might even countersue if A is right B attempted to harm A. There are practical legal solutions, rather than the risky enterprise of taking the law into your own hands: you could get a court order requiring B to receive their packages wherever they live.
You might be able to get away with it if there is a credible threat and end up getting sued, but not if you just have in mind annoying your spouse.