Wendy, I think you've gotten a ton of really good advice here. I also don't think Finn's behavior is abnormal - just closer to one end of the picky spectrum.
FWIW, my DD is like this and I am in the same situation as you except in our case, DH doesn't eat dinner with us (he'll sit with us but refuses to eat anything I cook and will not eat vegetables... don't get me started please...) so I am the only parent to set an example of healthy eating. At present (age 2.9) she will eat one vegetable (broccoli, but only with cheese), no meat (unless in a bolognese sauce), about 3 different fruits, and no dairy other than cheese. If it were up to her, she'd subsist on pasta and bread. I just hope it gets better but I'm not sure there's much I can do other than control *when* and *what* is served, set a good example, and keep encouraging and offering over and over and over.
The one thing I really want to say though is that, I think when it comes to food and trying new things, truly 'enforcing' the rule will backfire. I have no scientific basis for saying this, but it is a very strong intuition I have, having struggled with eating disorders most of my life. I think that with food it is extremely important to avoid getting into any power struggles and to keep emotions separate (don't use food as incentives or rewards or means of comfort, for example), and truly forcing him to try something could cause him to develop negative associations with the food or the act of trying something new. I think as long as he sees you eating a variety of healthy foods, and you're offering these foods to him in a positive environment, and you're giving him the chance to be hungry at mealtimes (no snacking, or at least limit snacking) eventually he will branch out.
Just my two cents. And, admittedly, my DD is a terrible eater so maybe I don't know what I'm talking about.
I know it is so incredibly frustrating. Good luck.