I really, REALLY sympathise. DS2 was like this and it is emotionally draining. Also in a fundamental way it feels as though they are rejecting your attempt to nurture them and enable them to thrive. I found it very tough watching other people;s children tucking in, or reading 'children will try new foods if you introduce them ten times, when I was the 100th time and counting!
Turned out our DS was autistic, which often shows in extremely limited eating habits. Now he is a young adult and really adventurous with food, loves cooking, eating out, trying new things.
My tips are:
Take ALL the stress out of it. Stop worrying. It doesn;t increase the chance of him eating more, but it makes you miserable and he'll pick up on it.
Let him eat what he eats. What you describe is reasonably healthy. I'd just make peanut butter sandwiches for him at breakfast, put a couple of chicken drumsticks in his packed lunch with some reasonably healthy snacks (the kind you normally don't give him - maybe Organix crunchy sticks or mini breadsticks with processed dipper cheese etc
Make cake if he eats cake. Make it with real butter, loads of eggs, half real flour and half almond or soy flour. Use cream cheese for the frosting. That way he's getting lots of calories and protein from the cake. I did this and then started sneaking in traces of veg - carrot cake, chocolate cake with courgette or beetroot in it - not too much - just tiny amounts.
Give daily vitamin chewy sweets of put abidec drops in his milk if he will drink milk.
Try going out for food. It's infuriating that they will eat a Happy Meal but gradually you can make your own burgers (with good meat, tiny amounts of grated veg etc.)
Teach him what food does. explain protein makes his muscles striong and dairy give him good bones and teeth, fish and veg make him clever and help him see and feel things etc. Just educate him and then leave stuff lying around casually. I used to leave carrot sticks, cubes of cheese, cucumber slices etc in little bowls near his plate and say 'You don't have to eat these but if you do, they'll help you see in the dark/ make your bones grow' etc.
Meanwhile you and Dh should eat what you want in front of him with great enjoyment and if he ever shows interest, offer him a tiny bit. You could try negative negotiation 'Oh no, you're not allowed this until you are a big boy' and see if it makes him curious.
Sorry for the essay. I tried everything I could think of, these are what worked.