Put the peppers under the broiler to blacken evenly all over; leave the oven door slightly ajar to allow steam to escape. (Alternatively char the peppers over an open flame on the stovetop.) Put the peppers in a bowl and cover with plastic wrap. Cool the peppers in order to handle, peel and seed.
Preheat a grill pan or griddle pan over medium-high heat.
Meanwhile, season the chicken with salt and pepper and dried herbs, and coat with a little extra-virgin olive oil. Season the shrimp with the seafood seasoning and toss with a little oil as well.
Coarse chop and put the red sweet peppers in a food processor with the vinegar, chilies, garlic and about 1/4 cup extra-virgin olive oil and puree into a sauce.
Grill the chicken 6 minutes on each side. Grill shrimp 3 minutes on each side. Toss the chicken and shrimp with the marinade and serve hot or cold or at room temperature.