Everyone else who has posted has given really good advice, especially MOM's point about your cat being motivated to adapt to the new behavior by being offered more tempting and attractive alternatives such as a taller cat tree in the kitchen area - where he can be comfy and lay there and still be part of the activity and see what is going on, from his own kitty area.
The main thing is that when you want to take away old behaviors from a kitty (the same as with a small child) you need to substitute new attractive rituals and behaviors. This is like the Nanny911 show
since working with cats and dogs is not unlike working with toddlers- except unfortunately we don't speak the same language so a lot depends on trying hard to understand their needs -and vice versa.
Ask yourself what motivated the cat to do his old behavior? In the kitchen when he laid on the counter or in the sink he wanted to be up with the people and hang with them at their level.
In the cupboards he probably was bored and wanted to play - so that means he needs some toys, preferably a stick with a string on it and a toy at the end of it, that he can chase around, or a laser light to wear out his energy and curiousity. And he NEEDS play sessions at regulated times.
Cats are creatures of habit and ritual. If we do not give them structure and activity that is suited to our routine, they will make their own. My advice is to structure his play sessions to suit your routine, so long as you make sure they are around the same time each day, and that you follow them the same as you would with a child. Like a child your kitty will not be perfect but he will adapt to the new routines.
As far as stopping the old behavior, if NO does not work (someone also mentioned a jar of coins and that is extremely effective too!) I use a water spray bottle to keep my kitty off the kitchen counter when there is food around. Some people do not recommend this, because the cat will associate YOU with the water bottle and will avoid you- unless you are really committed to winning his love and you are sure to set up the play routines and give treats when he does the right thing, and indeed to substitute the other attractive things that MOM mentioned in her post. I would try the other things first by all means. If you DO resort to the water bottle along with strong NO's, know that after one or two sprays you only need to show them the spray bottle.
Finally, like the others who posted, I accept that the cats live here too and it is likely when I am not home they will roam in the places they are not supposed to be around. It sounds like your hubby more or less hung with your kitty like a roommate and was more of a pal instead of being a father/parent to the little guy.
You could make this little kitty boy a happy little boy indeed if you take an interest in him and his new routine: buy him some flat cardboards (at PetCo or PetSmart) to use for his paws and sprinkle catnip on them so he knows they are his and put them in what you would like to be his territory; get him some kitty beds or mats and place them where you want him to sleep (but preferably high up- lots of cats sleep on the backs of the upper sofa cushions and it would be good to have one or two mats there).
Buy his toys - little cloth mice, the string and stick, some of those colored crackle balls and make a great show of introducing them to him and using his name a lot and what a good boy he is. When you play with him, egg him on with lots of "get it!'s" and he will indeed respond.
For his litter box, get the "astro turf" mats they sell at Home Depot and use those so that he will not track litter beyond where you want it to go.
You don't have to explain about this new situation you find yourself in. It is probably something you didn't expect but just the fact that you have signed up to this forum and are asking for advice shows that your heart is in the right place and you are ready to be proactive and make this a win-win situation for everyone.
Good luck and please do post back on your progress. I am hopeful that your new little boy and you will be best buddies and he will be very happy with you as his new mommy.