Combine all ingredients except oils in a processor. Slowly add oils in a steady stream with motor running until emulsified. Dressing can be made in advance and refrigerated in an airtight container for several days.
Preheat oven to 350 degrees. Rub chicken breasts with salt and pepper and olive oil. Cook 25 min until 165 degrees internal temperature is reached. Meanwhile, heat beans in small pan; season to taste with a pinch of salt and pepper.
In a large bowl, combine lettuces, tomatoes, cilantro and onions. Toss with enough dressing to coat, as desired.
To assemble, place tostada shells on serving plates, spread with warm beans, 2 oz of cheese, 1/3 lb chicken and 2 oz shrimp. Divide lettuce mixture among plates, top with a spoonful of salsa, as desired, and a pinch of cheese and onion. Serve with avocado and lime on the side.
*Shredded Market Rotisserie Chicken can be substituted.