Place the potatoes in a steamer basket set over boiling water. Steam until tender, about 15 to 25 minutes. Transfer the potatoes to a large bowl and toss with lemon juice, salt and pepper. Cover with plastic wrap and refrigerate until completely cool.
Meanwhile, steam the asparagus until bright green and tender crisp, about 3 to 5 minutes. Transfer to a colander and rinse under cold running water until cool. In a small bowl, combine the mayonnaise, yogurt and mustard.
To serve, gently toss together the cooled potatoes, asparagus and green onions. Drizzle the mayonnaise mixture over the salad, tossing just until everything is coated with dressing. Sprinkle with parsley and serve immediately or refrigerate for up to 2 hours before serving.