Melt the butter with the olive oil in a skillet over medium-high; stir the parsley, basil, oregano, garlic, salt, lemon juice, and wine into the butter mixture. Add the chicken; cook and stir until the chicken is browned, about 3 minutes. Reduce heat to medium; cook, stirring occasionally, until the chicken is no longer pink inside, about 10 more minutes.
Add the asparagus; cook and stir until the asparagus is bright green and just starting to become tender, about 3 minutes. Stir in the mushrooms and cook an additional 3 minutes to let the mushrooms release their juice. Serve hot.
