Make the marinade. In a large bowl, whisk together the sherry vinegar, olive oil, garlic, paprika, oregano, salt, and black pepper.
Marinate the meat. Divide the marinade between the steak and chicken, making sure each piece is well coated. Cover and refrigerate for at least 1 hour, or up to 8 hours.
Prepare the vegetables. Cut the peppers and red onion into pieces roughly the same size as the meat. If using wooden skewers, soak them in water for at least 30 minutes.
Build the kabobs. Thread the steak, chicken, peppers, and red onion onto the skewers, alternating the ingredients. Avoid packing everything too tightly so the meat can cook evenly.
Grill the kabobs. Preheat the grill to medium-high heat. Lightly oil the grates, then place the kabobs on the grill. Cook, turning every few minutes, until the vegetables are charred and the chicken and steak are cooked to your desired doneness. The chicken should reach an internal temperature of 165°F.
Rest and serve. Remove the kabobs from the grill and let them rest for about 5 minutes before serving. Serve hot with your favorite Spanish-inspired sides.