Heat the oven and pan. Preheat the oven to 425°F and place a large rimmed sheet pan inside while it heats so the hot pan helps the food brown faster.
Make the balsamic mixture. In a small bowl, whisk together olive oil, balsamic vinegar, Dijon mustard, honey, garlic, Italian seasoning, salt, and pepper until glossy.
Prep the main ingredients. Pat the chicken thighs dry with paper towels, slice the sausage into coins, and cut the peppers, zucchini, and onion into similar-sized pieces.
Coat the vegetables and sausage. In a large bowl, toss the peppers, zucchini, onion, and sausage with about two thirds of the balsamic mixture.
Arrange the pan. Carefully remove the hot sheet pan, spread the vegetable and sausage mixture over it, then rub the remaining balsamic mixture mostly on the meat side of the chicken and place the thighs skin side up on top.
Roast. Roast for 18 to 22 minutes, until the chicken reaches 175°F to 185°F in the thickest part, the sausage is browned at the edges, and the vegetables are tender with some dark spots.
Broil if needed. For deeper color, broil for 1 to 2 minutes at the end, watching closely because the balsamic can scorch quickly.
Rest and serve. Rest the chicken for 5 minutes, squeeze lemon over the pan if using, and serve with the sticky balsamic bits scraped from the pan.