Preheat grill. Mix tomatoes, onions, peppers, cilantro, jalapeno, and 1/4 teaspoon salt in a bowl. Allow to sit for 1/2 hour. Pour off juice and add honey and vinegar. Refrigerate 1/2 hour.
Rub mushrooms with oil and season with salt and pepper. Grill on both sides until done. Season burgers and grill on both sides until medium rare.
Layer with portobello on the bottom, salsa, then meat and topped with additional salsa.