Preheat oven to 350 F.
In a bowl, combine the chopped lettuce, tomato, peppers, and jalapenos.
Add in 1/2 cup of the mayonnaise along with the Italian seasoning, olive oil and balsamic vinegar. Stir well. Refrigerate until ready to use.
Cut the buns in half horizontally, trying to keep the two halves intact.
Transfer the bread to the baking sheet, with the bun bottoms cut-side up and the bun tops cut-side down.
Top the bun bottoms with the meats. Add cheese slices.
Bake for 10 minutes, just long enough to get the bread warm and a little toasted, and just starting to melt the cheese.
Add salad mixture to bun bottoms and spread out evenly, all the way to the edges.
Slather the cut-side of the bun tops with the remaining mayonnaise.
Place bun tops on the sandwich and transfer to a cutting board.
Cut into individual sliders and serve.