Cook and stir the beef and pork mince and in a large pot over medium-high heat until lightly browned. Drain any excess grease, then stir in the onion, mushrooms and garlic. Cook and stir until the onion has softened and turned translucent, about 5 minutes more.
Stir in the chipotle chilli, tomato paste and stewed tomatoes. Bring to a simmer then reduce heat to medium-low and simmer for 15 minutes. Season to taste with salt and pepper then stir in the basil and oregano; simmer 5 minutes more then remove from the heat.
While the sauce is simmering, stir together the cream cheese and chopped spinach until blended. Leave the spinach soggy, the water will help thin out the cream cheese to a sour cream-like consistency.
Preheat oven to 200 degrees C.
Line the bottom of a 20x30cm baking dish with a sheet of aluminium foil and lightly grease. Place 3 sheets lasagne on the bottom of the pan and spread with 1/3 of the spinach mixture. Spread 1/3 of the chipotle meat sauce over this, then layer with 1/3 of the mozzarella and 1/3 of the zucchini. Sprinkle with 1/3 of the Asiago cheese and 1/3 of the Parmesan cheeses. Repeat layers two more times, ending with cheeses on top.
Cover the dish with aluminium foil and bake in preheated oven for 40 minutes. Uncover and continue baking until the top is bubbly and golden brown, 15 to 20 minutes.