Combine the mustard, honey, mayonnaise, and lemon juice in a small bowl. Place chicken in a Ziploc bag and pour in about 1/3 of the marinade. Seal the bag and marinate in the refrigerator for about 2 hours. Chill the remaining marinade until later. After the chicken has marinated, remove chicken from bag and discard the marinade that it has been soaking in.
Preheat the oven to 375 degrees and heat an ovenproof frying pan large enough to hold all four breasts. Sear the chicken in 1 tablespoon oil in the pan for 3-4 minutes per side or until golden brown. Remove from heat but keep chicken in the pan.
Saute the mushrooms in butter in a small skillet. Brush each seared chicken breast with a little of the honey mustard marinade, reserving some to serve on the side later with the dish. Season the chicken with salt, pepper and paprika. Stack two pieces of cooked bacon, crosswise on each chicken breast. Spoon the sauteed mushrooms onto the bacon, being sure to coat each breast evenly. Sprinkle 1/4 cup Monterey Jack cheese evenly onto each breast followed by 1/4 cup of cheddar. Bake chicken breasts until cheese is thoroughly melted and starting to bubble, about 10 minutes. Sprinkle with parsley before serving and serve honey mustard marinade on the side.